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In vector calculus, del is a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), del may denote the gradient (locally steepest slope) of a scalar field, the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.

Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product of scalars, dot product, and cross product, respectively, of the del "operator" with the field. These formal products do not necessarily commute with other operators or products.

Definition[link]

In the three-dimensional Cartesian coordinate system R³ with coordinates (x, y, z), del is defined in terms of partial derivative operators as

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla = \mathbf{\hat{x}} {\partial \over \partial x} + \mathbf{\hat{y}} {\partial \over \partial y} + \mathbf{\hat{z}} {\partial \over \partial z}

where Failed to parse (Missing texvc executable; please see math/README to configure.): \{\mathbf{\hat{x}}, \mathbf{\hat{y}},\mathbf{\hat{z}} \}

are the unit vectors in their respective directions.

Though this page chiefly treats del in three dimensions, this definition can be generalized to the n-dimensional Euclidean space Rⁿ. In the Cartesian coordinate system with coordinates (x₁, x₂, ..., x_n), del is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla = \sum_{i=1}^n \hat e^i {\partial \over \partial x_i}

where Failed to parse (Missing texvc executable; please see math/README to configure.): \{ \hat e^i: 1\leq i\leq n\}

is the standard basis in this space.

More compactly, using the Einstein summation notation, del is written as

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla = \hat e^i \,\partial_i

Del can also be expressed in other coordinate systems, see for example del in cylindrical and spherical coordinates.

Notational uses[link]

Del is used as a shorthand form to simplify many long mathematical expressions. It is most commonly used to simplify expressions for the gradient, divergence, curl, directional derivative, and Laplacian.

Gradient[link]

The vector derivative of a scalar field f is called the gradient, and it can be represented as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla f = {\partial f \over \partial x} \mathbf{\hat{x}} + {\partial f \over \partial y} \mathbf{\hat{y}} + {\partial f \over \partial z} \mathbf{\hat{z}}

It always points in the direction of greatest increase of f, and it has a magnitude equal to the maximum rate of increase at the point—just like a standard derivative. In particular, if a hill is defined as a height function over a plane h(x,y), the 2d projection of the gradient at a given location will be a vector in the xy-plane (sort of like an arrow on a map) pointing along the steepest direction. The magnitude of the gradient is the value of this steepest slope.

In particular, this notation is powerful because the gradient product rule looks very similar to the 1d-derivative case:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla(f g) = f \nabla g + g \nabla f

However, the rules for dot products do not turn out to be simple, as illustrated by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla (\vec u \cdot \vec v) = (\vec u \cdot \nabla) \vec v + (\vec v \cdot \nabla) \vec u + \vec u \times (\nabla \times \vec v) + \vec v \times (\nabla \times \vec u)

Divergence[link]

The divergence of a vector field Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{v}(x, y, z) = v_x \mathbf{\hat{x}} + v_y \mathbf{\hat{y}} + v_z \mathbf{\hat{z}}

is a scalar function that can be represented as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,\vec v = {\partial v_x \over \partial x} + {\partial v_y \over \partial y} + {\partial v_z \over \partial z} = \nabla \cdot \vec v

The divergence is roughly a measure of a vector field's increase in the direction it points; but more accurately, it is a measure of that field's tendency to converge toward or repel from a point.

The power of the del notation is shown by the following product rule:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \cdot (f \vec v) = f \nabla \cdot \vec v + \vec v \cdot \nabla f

The formula for the vector product is slightly less intuitive, because this product is not commutative:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \cdot (\vec u \times \vec v) = \vec v \cdot \nabla \times \vec u - \vec u \cdot \nabla \times \vec v

Curl[link]

The curl of a vector field Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{v}(x, y, z) = v_x\mathbf{\hat{x}} + v_y\mathbf{\hat{y}} + v_z\mathbf{\hat{z}}

is a vector function that can be represented as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\;\vec v = \left( {\partial v_z \over \partial y} - {\partial v_y \over \partial z} \right) \mathbf{\hat{x}} + \left( {\partial v_x \over \partial z} - {\partial v_z \over \partial x} \right) \mathbf{\hat{y}} + \left( {\partial v_y \over \partial x} - {\partial v_x \over \partial y} \right) \mathbf{\hat{z}} = \nabla \times \vec v

The curl at a point is proportional to the on-axis torque to which a tiny pinwheel would be subjected if it were centered at that point.

The vector product operation can be visualized as a pseudo-determinant:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times \vec v = \left|\begin{matrix} \mathbf{\hat{x}} & \mathbf{\hat{y}} & \mathbf{\hat{z}} \\[2pt] {\frac{\partial}{\partial x}} & {\frac{\partial}{\partial y}} & {\frac{\partial}{\partial z}} \\[2pt] v_x & v_y & v_z \end{matrix}\right|

Again the power of the notation is shown by the product rule:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times (f \vec v) = (\nabla f) \times \vec v + f \nabla \times \vec v

Unfortunately the rule for the vector product does not turn out to be simple:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times (\vec u \times \vec v) = \vec u \, \nabla \cdot \vec v - \vec v \, \nabla \cdot \vec u + (\vec v \cdot \nabla) \vec u - (\vec u \cdot \nabla) \vec v

Directional derivative[link]

The directional derivative of a scalar field f(x,y,z) in the direction Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{a}(x,y,z) = a_x \mathbf{\hat{x}} + a_y \mathbf{\hat{y}} + a_z \mathbf{\hat{z}}

is defined as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{a}\cdot\mbox{grad}\,f = a_x {\partial f \over \partial x} + a_y {\partial f \over \partial y} + a_z {\partial f \over \partial z} = (\vec a \cdot \nabla) f

This gives the change of a field f in the direction of a. In operator notation, the element in parentheses can be considered a single coherent unit; fluid dynamics uses this convention extensively, terming it the convective derivative—the "moving" derivative of the fluid.

Laplacian[link]

The Laplace operator is a scalar operator that can be applied to either vector or scalar fields; it is defined as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta = {\partial^2 \over \partial x^2} + {\partial^2 \over \partial y^2} + {\partial^2 \over \partial z^2} = \nabla \cdot \nabla = \nabla^2

The Laplacian is ubiquitous throughout modern mathematical physics, appearing in Laplace's equation, Poisson's equation, the heat equation, the wave equation, and the Schrödinger equation—to name a few.

Tensor derivative[link]

Del can also be applied to a vector field with the result being a tensor. The tensor derivative of a vector field Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{v}

is a 9-term second-rank tensor, but can be denoted simply as Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \otimes \vec{v}

, where Failed to parse (Missing texvc executable; please see math/README to configure.): \otimes

represents the dyadic product. This quantity is equivalent to the transpose of the Jacobian matrix of the vector field with respect to space.

For a small displacement Failed to parse (Missing texvc executable; please see math/README to configure.): \delta \vec{r} , the change in the vector field is given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \delta \vec{v} = (\nabla \otimes \vec{v}) \sdot \delta \vec{r}

Second derivatives[link]

DCG chart: A simple chart depicting all rules pertaining to second derivatives. D, C, G, L and CC stand for divergence, curl, gradient, Laplacian and curl of curl, respectively. Arrows indicate existence of second derivatives. Blue circle in the middle represents curl of curl, whereas the other two red circles(dashed) mean that DD and GG do not exist.

When del operates on a scalar or vector, generally a scalar or vector is returned. Because of the diversity of vector products (scalar, dot, cross) one application of del already gives rise to three major derivatives: the gradient (scalar product), divergence (dot product), and curl (cross product). Applying these three sorts of derivatives again to each other gives five possible second derivatives, for a scalar field f or a vector field v; the use of the scalar Laplacian and vector Laplacian gives two more:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{grad}\,f ) = \nabla \cdot (\nabla f)

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\,(\mbox{grad}\,f ) = \nabla \times (\nabla f)

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta f = \nabla^2 f

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{grad}\,(\mbox{div}\, \vec v ) = \nabla (\nabla \cdot \vec v)

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{curl}\,\vec v ) = \nabla \cdot (\nabla \times \vec v)

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\,(\mbox{curl}\,\vec v ) = \nabla \times (\nabla \times \vec v)

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta \vec v = \nabla^2 \vec v

These are of interest principally because they are not always unique or independent of each other. As long as the functions are well-behaved, two of them are always zero:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\,(\mbox{grad}\,f ) = \nabla \times (\nabla f) = 0

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{curl}\,\vec v ) = \nabla \cdot \nabla \times \vec{v} = 0

Two of them are always equal:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{grad}\,f ) = \nabla \cdot (\nabla f) = \nabla^2 f = \Delta f

The 3 remaining vector derivatives are related by the equation:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times \nabla \times \vec{v} = \nabla (\nabla \cdot \vec{v}) - \nabla^2 \vec{v}

And one of them can even be expressed with the tensor product, if the functions are well-behaved:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla ( \nabla \cdot \vec{v} ) = \nabla \cdot (\nabla \otimes \vec{v})

Precautions[link]

Most of the above vector properties (except for those that rely explicitly on del's differential properties—for example, the product rule) rely only on symbol rearrangement, and must necessarily hold if del is replaced by any other vector. This is part of the tremendous value gained in representing this operator as a vector in its own right.

Though you can often replace del with a vector and obtain a vector identity, making those identities intuitive, the reverse is not necessarily reliable, because del does not often commute.

A counterexample that relies on del's failure to commute:

Failed to parse (Missing texvc executable; please see math/README to configure.): (\mathbf u \cdot \mathbf v) f = (\mathbf v \cdot \mathbf u) f

Failed to parse (Missing texvc executable; please see math/README to configure.): (\nabla \cdot \mathbf v) f \ne (\mathbf v \cdot \nabla) f

Failed to parse (Missing texvc executable; please see math/README to configure.): (\nabla \cdot \mathbf v) f = (\frac{\part v_x}{\part x}+\frac{\part v_y}{\part y}+\frac{\part v_z}{\part z})f =

Failed to parse (Missing texvc executable; please see math/README to configure.): = \frac{\part v_x}{\part x}f+\frac{\part v_y}{\part y}f+\frac{\part v_z}{\part z}f

Failed to parse (Missing texvc executable; please see math/README to configure.): (\mathbf v \cdot \nabla) f = (v_x \frac{\part}{\part x}+v_y \frac{\part}{\part y}+v_z \frac{\part}{\part z})f =

Failed to parse (Missing texvc executable; please see math/README to configure.): = v_x \frac{\part f}{\part x}+v_y \frac{\part f}{\part y}+v_z \frac{\part f}{\part z}

A counterexample that relies on del's differential properties:

Failed to parse (Missing texvc executable; please see math/README to configure.): (\nabla x) \times (\nabla y) = (\mathbf{\hat x} \frac{\part x}{\part x}+\mathbf{\hat y} \frac{\part x}{\part y}+\mathbf{\hat z} \frac{\part x}{\part z}) \times (\mathbf{\hat x} \frac{\part y}{\part x}+\mathbf{\hat y} \frac{\part y}{\part y}+\mathbf{\hat z} \frac{\part y}{\part z}) =

Failed to parse (Missing texvc executable; please see math/README to configure.): = (\mathbf{\hat x} \cdot 1 +\mathbf{\hat y} \cdot 0+\mathbf{\hat z} \cdot 0) \times (\mathbf{\hat x} \cdot 0+\mathbf{\hat y} \cdot 1+\mathbf{\hat z} \cdot 0) =

Failed to parse (Missing texvc executable; please see math/README to configure.): = \mathbf{\hat x} \times \mathbf{\hat y} = \mathbf{\hat z}

Failed to parse (Missing texvc executable; please see math/README to configure.): (\mathbf u x )\times (\mathbf u y) = x y (\mathbf u \times \mathbf u) = x y \mathbf 0 = \mathbf 0

Central to these distinctions is the fact that del is not simply a vector; it is a vector operator. Whereas a vector is an object with both a precise numerical magnitude and direction, del does not have a precise value for either until it is allowed to operate on something.

For that reason, identities involving del must be derived with care, using both vector identities and differentiation identities such as the product rule.

See also[link]

• Del in cylindrical and spherical coordinates
• Maxwell's equations
• Navier–Stokes equations
• Table of mathematical symbols
• Vector calculus identities

References[link]

• Schey, H. M. (1997). Div, Grad, Curl, and All That: An Informal Text on Vector Calculus. New York: Norton. ISBN 0-393-96997-5. 
• Miller, Jeff. "Earliest Uses of Symbols of Calculus". http://jeff560.tripod.com/calculus.html. 
• "History of Nabla". netlib.org. January 26, 1998. http://www.netlib.org/na-digest-html/98/v98n03.html#2. 

External links[link]

• A survey of the improper use of ∇ in vector analysis (1994) Tai, Chen

Lana Del Rey
Del Rey at a promotional event in Seattle
Background information
Birth name	Elizabeth Woolridge Grant
Also known as	Lizzy Grant Lana Rey Del Mar May Jailer
Born	(1986-06-21) June 21, 1986 (age 26)[1] New York City, New York, United States
Origin	Lake Placid, New York, United States
Genres	Indie pop,[2] adult alternative,[2] chamber pop,[3] sadcore[4]
Occupations	Singer-songwriter, fashion model
Instruments	Vocals, guitar[5]
Years active	2007–present
Labels	Interscope, Polydor, Stranger
Website	lanadelrey.com

Elizabeth Woolridge Grant^[6] (born June 21, 1986), better known by her stage name Lana Del Rey, is an American singer-songwriter. Raised in upstate New York, Del Rey moved to New York City at age eighteen, where she attended college and began writing music and performing in clubs.

In 2008, Del Rey contracted with an independent label and recorded a self-titled debut album which was briefly available on iTunes in 2010; Del Rey ultimately bought back the rights to the album and it was withdrawn soon after.

In June 2011, she released the song "Video Games" on the Internet, accompanied by a self-made music video that went viral in the following months. The song was later released as a single in October, leading up to Del Rey's major-label debut album, Born to Die, which was released on January 31, 2012 through Interscope Records. Born to Die debuted at number one in seven countries, including the United Kingdom^[7] and Australia. The album has spawned two worldwide top 10 hits: "Video Games" and "Born to Die".

Del Rey's music has been noted for its cinematic sound and its references to various aspects of pop culture, particularly that of 1950s and '60s Americana.^[8] Del Rey has been described as a "self-styled gangsta Nancy Sinatra",^[9] and cites Britney Spears,^[10][11][12] Eminem,^[13][10] and Antony and the Johnsons amongst her musical influences.^[10]

Biography[link]

Early years[link]

Del Rey was born Elizabeth Grant in New York City and grew up in Lake Placid, New York.^[14][15] When she was 14, she attended Kent School, a boarding school in Connecticut.^[16][17] She has Scottish ancestry, and is the daughter of domain investor Rob Grant, who supported her in her early career as a singer.^{[18][19][20][21]} Del Rey attended Fordham University in New York City, studying philosophy.^[22]

At age 18, her uncle taught her how to play guitar, beginning with basic chords: "It was G, C, A, D minor, A minor and some diminished chord as well. Some trick, some shortcut," Del Rey recalled. "I realized I could probably write a million songs with those six chords, so I moved to New York and I took a couple of years to just write whatever I wanted."^[5] She began performing in clubs while living in the city.

Her stage name was discussed in a Vogue interview, in which she said, "I wanted a name I could shape the music towards [...] I was going to Miami quite a lot at the time, speaking a lot of Spanish with my friends from Cuba – Lana Del Rey reminded us of the glamour of the seaside. It sounded gorgeous coming off the tip of the tongue."^[23] The name is reportedly an amalgam of the actress Lana Turner, and the 1980's automobile Ford Del Rey. ^[24]

"I wanted to be part of a high-class scene of musicians. It was half-inspired because I didn't have many friends, and I was hoping that I would meet people and fall in love and start a community around me, the way they used to do in the '60s."^[25]

Del Rey first released a three-track EP titled Kill Kill in October 2008 under the name Lizzy Grant, featuring the tracks "Kill Kill", "Yayo" and "Gramma (Blue Ribbon Sparkler Trailer Heaven)".^[26]

[edit] 2010: Lana Del Ray A.K.A. Lizzy Grant

Del Rey later released her first full-length studio album titled Lana Del Ray A.K.A. Lizzy Grant [sic] in January 2010.^[27] It was the singer's first professionally produced album, released under Lizzy Grant on an independent label with producer David Kahne.^[28] Del Rey stated that "David asked to work with me only a day after he got my demo. He is known as a producer with a lot of integrity and who had an interest in making music that wasn't just pop."^[29] Her father, Robert Grant, helped with the marketing of the album,^[30] which was available for purchase on iTunes for a brief period before being withdrawn. According to David Kahne, who produced Grant, Grant bought the rights back from her label, 5 Points, as she wanted it out of circulation to "…stifle future opportunities to distribute it – an echo of rumors that the action was part of a calculated strategy."^[31]

[edit] 2011–present: Born to Die

Lana Del Rey performing at Paradiso, Amsterdam.

Later in June 2011, Del Rey was signed with Stranger Records,^[32] to release her debut single "Video Games";^[32] in October 2011, she signed a joint deal with Interscope Records and Polydor.^{[5][33][34][35]} In October 2011, she won the Q award for "Next Big Thing". Del Rey's song "Video Games" was featured for the first time on The CW's TV-Series Ringer on September 27, 2011.^[36] Del Rey also promoted the album in a number of live appearances, including a show at the Bowery Ballroom, where, according to Eliot Glazer of New York, "the polarizing indie hipstress brought her 'gangsta Nancy Sinatra' swagu."^[37] Rolling Stone commented that, despite Del Rey being nervous and anxious while performing her songs live, she "sang with considerable confidence", although they noted that "her transitions ...could be rather jarring."^[38] Del Rey also performed "Video Games" on Dutch television program De Wereld Draait Door,^[39] on British music television show Later... with Jools Holland,^[40] and on an intimate show at Chateau Marmont in West Hollywood, California.^[41]

Born to Die was released on January 27, 2012 in Ireland,^[42] January 30, 2012, in the UK, and on January 31, 2012 worldwide.^[43]

Del Rey performed two songs on Saturday Night Live on January 14, 2012 to a warm reception from the audience, but mixed reviews from critics and the general public. NBC Nightly News anchor Brian Williams called Del Rey's performance "one of the worst outings in SNL history". Del Rey's performance was defended by the evening's program guest host, actor Daniel Radcliffe, despite not having seen her performance.^[44] He said in part: "It was unfortunate that people seemed to turn on her so quickly [...] I don't think [the performance] warranted anywhere near that reaction." Del Rey had earlier defended her spot on the program, saying: "I'm a good musician [...] I have been singing for a long time, and I think that [SNL creator] Lorne Michaels knows that [...] it's not a fluke decision."^[45] On February 4, 2012, Kristen Wiig appeared on the Weekend Update segment on Saturday Night Live parodying Del Rey and poking fun at the backlash.

The second single and title track "Born to Die" was released on December 3, 2011.^[46] The music video for it leaked on December 14, 2011,^[47] and was based on a concept created by the singer, while being directed by Yoann Lemoine.^[48]

In January 2012, Del Rey revealed that she recently bought back the rights to her 2010 album Lana Del Ray A.K.A. Lizzy Grant and will re-release it in the summer of 2012 under Interscope Records and Polydor.^[49] Contrary to Grant's press statement, her previous label (5 Point Records), and producer David Kahne have both stated that she bought the rights to the album when she and the label parted company, due to the offer of a new deal, in April 2010.^[50][51] On January 4, 2012, it was reported she had signed a deal with NEXT Model Management agency.^[52] In May 2012, Del Rey confirmed the song "National Anthem" as the fourth single from her album Born to Die. ^{[53] [54]} On May 30th, 2012, Del Rey's supposed debut album "Sirens" was leaked online under the name "May Jailer". The 15 track album includes the previously leaked song "A Star for Nick."

Artistry[link]

Music

She has been described as a "self-styled gangsta Nancy Sinatra",^[9] Del Rey is known to write and produce most of her own material and covers genres from Hip-Hop and Indie. Having first been discovered from posting viral videos of herself singing on the internet she quickly grew a significant fan base. She has been noted for using her allure to the celebrity lifestyle as an inspiration in itself, whilst at the same time maintaining an aura of mystique, this has reflected in the melodies and vocals she produces. Her sound as well as her videography has been described as eccentric, over the top and at times wild. However Noah Levy, senior news editor at In Touch Weekly magazine noted that her dedication and talent is undeniable, quoted as saying "I think she cares about the art that she is creating. I don't think that is fake at all."^[55]

Voice

Del Rey possesses a wide^[56] contralto vocal range,^{[57][58][59][60]} which has been described as unique, captivating and highly emotive,^[60] being able to transcend from sounding high and girlish in her timbre, down to a low and jazzy sound with great ease, although both these areas of the voice can be conflicting in their sound and polarise opinion.^[57]

When recording in the studio Del Rey is known for vocal multi layering, double tracking and overlays which has it has been noted is difficult for her to replicate within a live setting, especially with the lack of backing singers to fill out the original vocal style.^[59].

Influences

Del Rey cites Britney Spears,^[11][12] Elvis Presley, Antony and the Johnsons, Frank Sinatra ^[13] and Eminem amongst her musical influences. "[I really] just like the masters of every genre", she told BBC journalist Jo Whiley.^[61]

Discography[link]

Albums[link]

• Lana Del Ray A.K.A. Lizzy Grant (2010)
• Born To Die (2012)

Awards and nominations[link]

References[link]

External links[link]

Wikimedia Commons has media related to: Lana Del Rey

• Official website
• Lana Del Rey at the Internet Movie Database
• Lana Del Rey talks influences with BEAT

Rob Van Dam
Van Dam in February 2005.
Ring name(s)	Robbie V[1][2] Rob Van Dam[1][2] Rob Szatkowski[2] Rob Zakowski[2]
Billed height	6 ft 0 in (1.83 m)[1][3]
Billed weight	237 lb (108 kg)[3]
Born	(1970-12-18) December 18, 1970 (age 41)[1] Battle Creek, Michigan[1][2]
Resides	Los Angeles, California[1]
Billed from	Battle Creek, Michigan[4]
Trained by	The Sheik[1][2]
Debut	1990[1][2]

Robert Alexander Szatowski^[1][2] (born December 18, 1970),^[1][2] better known by his ring name Rob Van Dam (RVD), is an American professional wrestler and actor. He is currently under contract with Total Nonstop Action Wrestling. He is best known for his time with World Wrestling Entertainment, and Extreme Championship Wrestling.

Szatkowski has held 22 championships between ECW, WWE and TNA, as well as several regional titles in various promotions during his career. He is a former WWE champion, ECW champion and the TNA World Heavyweight champion once each. On the independent scene he has also won the World Heavyweight Championships for both American Wrestling Rampage and World Stars of Wrestling once each. He is the only man to achieve both WWE and ECW's version of the Triple Crown. Part of ECW's Triple Crown included the ECW World Television Championship, of which RVD's 700 day reign was the longest.

Early life[link]

Szatkowski grew up in Battle Creek, Michigan and graduated from Pennfield High School. Rob made his first appearance on WWF television in 1987 in a skit with "The Million Dollar Man" Ted DiBiase. At the time, DiBiase was selecting plants from the audience and offering to pay them to perform degrading acts and offered the 16 year old Szatkowski $100 to enter the ring and kiss his foot, which he did.^[5] This early appearance was later included as a bonus feature on WWE's Before They Were Superstars DVD and on WWE's Rob Van Dam: One of a Kind DVD.^[6]

Professional wrestling career[link]

Early career (1990–1995)[link]

Szatkowski debuted in 1990 after being trained by The Sheik, wrestling his first match against Dango Nguyen in Toledo, Ohio. The name Rob Van Dam was given to Rob in 1991 by Ron Slinker, a promoter in Florida, possibly because of his martial arts experience and his resemblance to actor Jean-Claude Van Damme.^[7] He wrestled in many independent promotions across Michigan, including the United States Wrestling Association (USWA) and South Atlantic Pro Wrestling (SAPW). In SAPW, he won his first wrestling title, the SAPW Tag Team Championship, in July 1992 with Chaz Rocco.^[8] He signed with World Championship Wrestling in late 1992 and was dubbed Robbie V by Ron Slinker upon his arrival since Bill Watts didn't like the name Rob Van Dam. His WCW run was uneventful and largely unnoticed.^[9] He also wrestled in several independent promotions across America, and in All Japan Pro Wrestling, where he challenged for the AJPW World Junior Heavyweight Championship on several occasions.^[10]

Extreme Championship Wrestling[link]

Debut (1996)[link]

In January 1996 Van Dam signed with promoter Paul Heyman's Philadelphia-based promotion Extreme Championship Wrestling (ECW), defeating Axl Rotten in his debut match at House Party.^[11] Van Dam's mannerisms were those of a stoner, and he became a face due to his laid-back attitude and unorthodox style. On March 30, he faced 2 Cold Scorpio in a match for the ECW World Television Championship. The match ended in a draw with 2 Cold Scorpio retaining the title.^[12][13]

Van Dam gained attention following a series of matches with long-time rival Sabu, which began with a match at Hostile City Showdown, won by Sabu.^[14] After the match, Van Dam declined to show proper respect for his opponent, leading to a rematch at A Matter of Respect, which was won by Van Dam.^[13] Per the pre-match stipulation, Sabu then offered Van Dam a handshake, but was again ignored. Instead, Van Dam left the ring and turned heel under the management of Bill Alfonso.^[13][15] At Hardcore Heaven, Van Dam faced his rival Sabu once again, in a match to prove who was the better man. Sabu won the match.^[13][16] The two faced each other yet again in a stretcher match at The Doctor is In. Van Dam lost the match after missing a Plancha to the outside, hitting the railing and falling onto the stretcher.^[17] He was quickly rolled out.^[13]

Teaming with Sabu (1996–1998)[link]

At Natural Born Killaz, Van Dam defeated Doug Furnas in a match. Post-match, Van Dam offered Furnas a handshake, but Furnas instead hit Van Dam with a short-arm clothesline, starting a rivalry between the two.^[13] After his rivalry with Furnas expanded to also include Dan Kroffat, Van Dam wanted a tag team partner of his own. After losing to long-time rival Sabu once again at Unluckily Lottery, the two united and formed what was to become one of the most successful tag teams in ECW history.^[18] They feuded with Furnas and Kroffat defeating them at When Worlds Collide II and High Incident.^[13][19][20]

Van Dam and Sabu next feuded with The Eliminators, John Kronus and Perry Saturn. On November 1, the two teams fought to a draw.^[21] Van Dam then feuded with Taz, to whom he lost at Holiday Hell via knockout.^[22] Sabu and Van Dam continued to feud with The Eliminators for the ECW World Tag Team Championship into 1997. At Crossing the Line Again and Cyberslam, the teams faced off for the ECW World Tag Team Championship in a pair of matches, both of which were won by The Eliminators.^[23][24][25] At CyberSlam, the two teams faced each other for the title in a Tables, Ladders, and Chairs match, in which The Eliminators again retained their title.^[26]

At ECW's first pay-per-view event Barely Legal, Van Dam defeated Lance Storm as a last-minute replacement for the injured Chris Candido.^[27] Immediately following the match, Van Dam expressed his distaste for being chosen as a back-up for "some guy who couldn't even lace his boots". Van Dam delivered a speech directed towards Paul Heyman, and not being originally booked on the show was a point of contention between Van Dam and Heyman for a time.^[25]

In May 1997, ECW "invaded" the World Wrestling Federation's Monday Night Raw television show, drawing the ire of color commentator Jerry Lawler. Lawler then promised he would show up at an ECW show in order to gain revenge, and when he did show up, he had ECW mainstays Van Dam (who turned heel) and Sabu with him. Van Dam made speeches about how he was too good for ECW and deserved to be in one of the "Big Two" (WWF or WCW) on one of their Monday Night programs (Monday Night Raw or Monday Nitro). Lawler began to call Van Dam Mr. Monday Night on an episode of Raw which became a moniker that would stay with Van Dam, changing to suit the day of the week of whichever program was being broadcast. Despite his arrogance and "betrayal" of ECW, over time Van Dam became applauded by fans recognizing his athleticism and unique maneuvers.^[28]

Van Dam continued to team up with Sabu upon his return to ECW on June 13.^[29] Taz's manager Bill Alfonso betrayed Taz and joined Sabu and Van Dam. Van Dam started a new rivalry with Tommy Dreamer, who wanted to gain revenge on Van Dam for his betrayal of ECW.^[28][30] On June 21, Van Dam and Sabu earned a victory over Dreamer and The Sandman.^[31] Van Dam and Sabu emerged victorious against Dreamer and Sandman again at Orgy of Violence.^[32] At Heat Wave, Van Dam, Sabu, and WWF's Jerry "The King" Lawler fought Dreamer, Sandman, and Rick Rude to a no contest.^[33] Van Dam and Dreamer faced each other in a hardcore match at Born to Be Wired, won by Van Dam after he performed a leg drop on Dreamer with a trashcan.^[30][34] At As Good as it Gets, the team of Van Dam and Alfonso lost to Dreamer and Beulah McGillicutty in a mixed tag team match.^[30][35] Van Dam and Sabu became partners while Dreamer teamed up with Taz.^[30] At Fright Fight, Van Dam lost to Dreamer in a flag match.^[36] At Ultimate Jeopardy, Van Dam and Sabu faced Dreamer and Taz, a match won by Taz and Dreamer after Dreamer pinned Van Dam. At November to Remember, Van Dam faced Dreamer in another flag match which went to a no contenst.^[37] At Better Than Ever, Van Dam and Sabu faced Dreamer and Taz in a rematch. This time, Van Dam pinned Dreamer to give the victory to his team and to settle their rivalry.^[38] Van Dam's final encounter with Dreamer came on December 26, when Dreamer teamed up with Taz, Al Snow, and Sandman to take on Van Dam, Sabu, Doug Furnas, and Phil Lafon. Van Dam's team lost the match.^[39]

In 1998, Van Dam turned face and started a feud with Triple Threat (Shane Douglas, Bam Bam Bigelow, and Chris Candido).^[40] At House Party, Van Dam defeated Bam Bam Bigelow.^[41] At Hostile City Showdown, Van Dam and Sabu defeated Axl Rotten and Balls Mahoney by disqualification.^[42] The two went on to win a fatal four way elimination tag team match later that night.^[42] At CyberSlam, Van Dam and Sabu fell to Shane Douglas and Bam Bam Bigelow.^[43]

RVD as both ECW World Tag Team Champion with Sabu behind him, and ECW World Television Champion.

Van Dam's popularity increased when he got his first taste of ECW gold, on April 4 when he defeated Bam Bam Bigelow to win the ECW World Television Championship.^[44][45] Van Dam retained the belt in his first title defense on April 10 against Doug Furnas.^[46] Sabu also expressed interest in Van Dam's championship, leading to a title match between the two at Wrestlepalooza. Van Dam retained the title as the match ended in a time limit draw.^[40][47]

At A Matter of Respect, Van Dam and Sabu were forced to face each other in a tag team match as they both teamed up with ECW World Tag Team Champions. Van Dam teamed with the one half of the champions, Lance Storm, while Sabu teamed with the other half, Chris Candido. Van Dam and Sabu reconciled and instead took out Storm and Candido making it a no contest.^[40][48] Van Dam and Sabu started a feud with Storm and Candido in the next month for the tag team title.^[40] On June 27, Van Dam and Sabu beat Storm and Candido to win the ECW World Tag Team Championship,^[49] which made Van Dam a double champion.^[40] On October 24, Sabu and Van Dam lost the title to the Dudley Boyz (Buh Buh Ray and D-Von) after interference from Triple Threat.^[40][50] Van Dam sought revenge and at November to Remember, Van Dam and Sabu teamed with Taz to defeat Triple Threat.^[40][51] On December 13, Van Dam and Sabu won the ECW World Tag Team Championship for a second time by beating the Dudley Boyz in Japan at a Frontier Martial-Arts Wrestling (FMW) show.^[40][49]

World Television Champion (1998–2001)[link]

Van Dam remained the Television champion for the rest of 1998, and he started 1999 by making successful title defenses against the likes of Spike Dudley,^[52] Lance Storm at Guilty as Charged,^[53] Balls Mahoney,^[54] and 2 Cold Scorpio at CyberSlam.^[55][56]

Van Dam and Sabu were scheduled to make a title defense on April 17, but Sabu was suspended by ECW before the match occurred.^[56] Instead, Van Dam faced D-Von Dudley in a singles match and as a result of losing the match, Van Dam also lost the Tag Team Title to the Dudleyz.^[57] After losing the Tag Team titles, Van Dam focused on defending the Television title.^[56] He entered into a rivalry with Jerry Lynn against whom he defended the Television title at Hardcore Heaven in a "no time limit" match.^[58] Van Dam retained the title, and the match was deemed so good that Paul Heyman aired it on ECW's debut on TNN in place of a shoot promo about TNN that he was planning, but was not allowed to air.^[58] Van Dam continued to defend the ECW World Television Championship for the remainder of the year.

Van Dam began a feud with Rhino in the beginning of 2000. RVD successfully defended the ECW World Television Championship against Rhino on January 7.^[59] RVD got a big victory during a title defense against Sabu at Guilty as Charged.^[60][61] Van Dam was scheduled to perform in a "champion vs. champion" pay-per-view main event against ECW World Heavyweight Champion Mike Awesome. This match potentially could have been ECW's most lucrative pay-per-view main event, and Heyman was depending on it to bring an influx of badly needed finances, but the match never occurred because Van Dam suffered a broken ankle during a successful title defense against Rhino on January 29.^[60][62] The injury also forced Van Dam to vacate the ECW World Television Championship.

He returned to ECW at Hardcore Heaven and faced long-time rival Jerry Lynn. Van Dam was supported by his real-life friend Scotty Anton who eventually turned on him when Van Dam was going to perform a Five-Star Frog Splash on Lynn. Anton pushed him from the top rope, which helped Lynn win the match.^[60][63] Van Dam feuded with Anton and took his revenge at Heat Wave by defeating Anton after a Van Terminator.^[60][64] Van Dam then attempted to exact revenge on Rhino for forcing his injury. He received many opportunities to win the ECW World Television Championship back from Rhino, but Rhino's allies usually attacked Van Dam, causing disqualifications and allowing Rhino to retain the title.^[60] At Anarchy Rulz, Van Dam faced Rhino for the ECW World Television Championship but was screwed when a heel referee made a fast count during a pinfall attempt made by Rhino.^[60][65]

Van Dam was not advertised and did not show for a large number of ECW events due to the large sum of money owed to him.^[60] He appeared at ECW's final pay-per-view event Guilty as Charged, where he defeated Jerry Lynn.^[66][67] This was Van Dam's last appearance in ECW, as ECW only held two more shows after the pay-per-view.

World Wrestling Federation / Entertainment[link]

The Invasion (2001)[link]

Several months after the closure of ECW, Van Dam was signed to a short term contract by the World Wrestling Federation (WWF). Along with fellow ECW alumnus Tommy Dreamer, Van Dam returned to WWF television on the July 9, 2001 episode of Raw in Atlanta, Georgia as a heel, and attacking WWF wrestlers Kane and Chris Jericho.^[68][69] Later that night, five wrestlers from WWF and five wrestlers from WCW took on ten ECW wrestlers, including Van Dam. The match never took place as instead the WCW wrestlers aligned themselves with the ECW wrestlers.^[68][69]

Despite being a heel, Van Dam was popular with the WWF fans, who were aware of his reputation in ECW. After defeating Jeff Hardy for the WWF Hardcore Championship at Invasion,^[68][70][71] Van Dam became one of the most over members of the Alliance and even challenged Alliance leader Stone Cold Steve Austin for the WWF Championship including a triple threat match at No Mercy.^[68][72] Van Dam lost the Hardcore Title to Hardy on the August 13 episode of Raw,^[73] but regained the title from Hardy at SummerSlam.^[71][74] At Survivor Series on November 18, Van Dam and four other Alliance members faced five WWF wrestlers in a Winner Take All match. Team WWF won, and the members of the Alliance were fired; however, as he held the Hardcore Championship, Van Dam was able to retain his job.^[68][75]

Intercontinental Champion (2001–2002)[link]

Van Dam became a face but lost the Hardcore Championship to The Undertaker at Vengeance.^[76][77] He then entered into a rivalry with William Regal over Regal's Intercontinental title.^[78] On the February 25 episode of Raw, Van Dam defeated Lance Storm and Big Show in a triple threat match to become the #1 contender to the Intercontinental title.^[78][79] At WrestleMania X8, RVD faced Regal for the Intercontinental title and won the match after he hit Regal with a Five-Star Frog Splash.^[78][80][81]

Van Dam after winning the Intercontinental Championship at WrestleMania X8.

When the WWF was divided into two "brands", Raw and SmackDown! in 2002, Van Dam was drafted to the Raw brand as the fourth pick.^[82][83] After he defended his title successfully against Booker T, Eddie Guerrero returned to the WWF and attacked Van Dam.^[82][84] He started a feud with Eddie Guerrero over the Intercontinental title. At Backlash, Van Dam lost the Intercontinental Title to Guerrero.^[82][85] At Insurrextion, Van Dam and Guerrero had a rematch for the Intercontinental Title. Guerrero was disqualified after hitting the referee with the Intercontinental title; as a result, Van Dam won the match but not the title because a title cannot change hands by disqualification.^[82][86] At Judgment Day, Van Dam failed to win the Intercontinental Title in another rematch.^[82][87] The following night he defeated The Undertaker for the Undisputed Championship but authority figure Ric Flair restarted the match, which Van Dam then lost negating the title win.^[82][88] On the May 27 episode of Raw, Van Dam defeated Eddie Guerrero in a ladder match for the Intercontinental Title.^[82][89][90]

After facing each other in the final round of the King of the Ring tournament, Van Dam and Brock Lesnar began feuding with each other. Van Dam defended his Intercontinental Title against Lesnar twice and retained his title both times by disqualification.^[82][91][92] On July 21, 2002, Van Dam unified the WWE European Championship into the WWE Intercontinental Championship after he defeated European Champion Jeff Hardy in a title unification ladder match. As a result, the European title was abandoned. On the July 29 episode of Raw, Van Dam lost the Intercontinental title to Chris Benoit.^[82][93]

RVD as Intercontinental Champion

At SummerSlam, Van Dam won his third WWE Intercontinental Championship by defeating Benoit in a rematch for the title.^[82][94][95] As Benoit brought the title to SmackDown when he switched brands shortly after winning it, RVD brought the Intercontinental Title back to Raw.^[82] On the August 26 episode of Raw, Van Dam also unified the WWE Hardcore Championship into the WWE Intercontinental Championship by defeating Hardcore Champion Tommy Dreamer in a hardcore title unification match. As a result, the WWE Hardcore Championship was abandoned.^[71][82][96] On the September 9 episode of Raw, Van Dam became the number one contender to the World Heavyweight Championship by defeating Chris Jericho, Jeff Hardy, and Big Show in a fatal four-way elimination match.^[82][97]

Van Dam started feuding with the World Heavyweight Champion Triple H. On the September 16 episode of Raw, Van Dam lost the Intercontinental title to Chris Jericho after interference by Triple H.^[82][98] At Unforgiven, Van Dam faced Triple H for the World Heavyweight Championship. Due to Ric Flair's interference, Van Dam lost the match.^[82][99] At No Mercy, Van Dam got his revenge on Flair by defeating him.^[82][100] At Survivor Series, Van Dam participated in the first-ever Elimination Chamber match for Triple H's World Heavyweight Championship, but it was won by Shawn Michaels. During the match Rob Van Dam performed a Five-Star Frog Splash off of one of the pods/chambers onto Triple H accidentally landing with his knee onto HHH's throat.^[82][101]

Teaming and feuding with Kane (2002–2003)[link]

Van Dam appeared on the World Heavyweight Championship scene and also formed a tag team with Kane in October 2002.^[82] Van Dam defeated Jericho and Booker T in a Triple Threat match to become the number one contender for the World Heavyweight Championship.^[82][102] On the November 25 episode of Raw, Van Dam faced Michaels for the World Heavyweight Championship. Michaels was disqualified after Triple H hit RVD with a Pedigree.^[82][103] On the December 2 episode of Raw, Van Dam lost to Triple H in a #1 contender's match with World Heavyweight Champion Shawn Michaels acting as the special guest referee.^[82][104]

In 2003, Rob Van Dam continued to team up with Kane. RVD participated in the Royal Rumble, and was one of the final five participants before being tricked and eliminated by his tag team partner Kane. The two faced Lance Storm and William Regal at No Way Out for the World Tag Team Championship but failed to win the title when Kane mistakenly chokeslammed RVD.^[105] On the March 31 episode of Raw, Van Dam and Kane defeated World Tag Team Champions Lance Storm and Chief Morley and The Dudley Boyz in a 3-way elimination tag team match to win the World Tag Team Championship.^[106][107] At Backlash, Van Dam and Kane retained the titles against The Dudley Boyz with Morley as the special guest referee.^[108] At Insurrextion, Van Dam and Kane defended the World Tag Team title successfully against La Résistance,^[109][110] before losing the title to La Résistance at Bad Blood.^[109][111]

After Kane was forced to take his mask off when he lost to Triple H, he turned heel, and the team with RVD dissolved. The two then started feuding with each other.^[109] On the August 18 episode of Raw, Van Dam faced the Intercontinental Champion Christian for the title, but Kane interfered in the match and knocked Van Dam out after hitting him with a chair. Kane then took Van Dam to the backstage where he was restrained and was about to be set on fire. Kane changed his mind at the last minute, however, and said that he wasn't going to do what "they" want.^[112] Their rivalry led to a No Holds Barred match at SummerSlam, which Kane won.^[109][113] On the September 8 episode of Raw, the rivalry ended when Rob Van Dam defeated Kane, when Kane threw RVD through the Steel by mistake in a steel cage match. Eric Bischoff came out and restarted the match, saying RVD didn't escape through the door or climb out Bischoff ordered the referees to put Rob Van Dam's body back inside the cage Kane eventually hit a chokeslam from the side of the cage to pick up the victory.^[109][114]

In September 2003, Van Dam started feuding with both Christian and Chris Jericho over Christian's Intercontinental Title. On the September 15 episode of Raw, Van Dam faced Jericho in a number one contender's match for the title. The match ended in a double disqualification when Intercontinental Champion Christian interfered and hit both men with the title belt.^[109][115] At Unforgiven in a triple threat match between Jericho, Christian, and Van Dam, Christian retained his title.^{[109][116][117]} Van Dam, however, defeated Christian in a ladder match on the September 29 episode of Raw to win the Intercontinental Championship for a fourth time.^[118]

Various feuds (2003–2004)[link]

Van Dam entered into a rivalry with Chris Jericho in October 2003, and the two faced each other in several tag team matches.^[116] On the October 27 episode of Raw, Van Dam lost the Intercontinental title to Jericho. Van Dam reached the ropes when the challenger had him in the Walls of Jericho, but Eric Bischoff distracted the referee while Jericho dragged the champion back into the middle of the ring. Van Dam submitted and Jericho became the new champion.^{[109][116][119]} Austin came out and immediately ordered Jericho to face Van Dam in a rematch inside the Steel Cage for the title. Van Dam won the rematch and his fifth Intercontinental Championship.^{[116][119][120]}

Rob Van Dam at a SmackDown! live event.

At Survivor Series, Van Dam was pinned by Randy Orton during his traditional elimination match.^[109][121] As a result, Orton and Van Dam started feuding with each other over Van Dam's Intercontinental title.^[109] Van Dam lost the Intercontinental title to Orton at Armageddon after interference from Ric Flair.^{[109][116][122]} Van Dam went on to feud with both Orton and Evolution. On the January 12, 2004 episode of Raw, Van Dam faced Orton in a rematch for the Intercontinental title but lost the match.^[123][124]

Van Dam formed a tag team with Booker T. The two teamed for the first time on the January 19 episode of Raw when they defeated Christian and Matt Hardy to qualify for a battle royal where the winner of the battle royal would get the #30 spot in the 2004 Royal Rumble match.^[123][125] On the February 16 episode of Raw, Booker T and Van Dam defeated Evolution members Ric Flair and Batista to win the World Tag Team Championship.^[123][126] At WrestleMania XX, Booker and Van Dam defended the World Tag Team Championship in a fatal four-way elimination tag team match against the Dudley Boyz, La Résistance, and the team of Mark Jindrak and Garrison Cade.^[123][127] On the March 22 episode of Raw, Booker T and Van Dam lost the World Tag Team Championship back to Evolution.^[123][128]