Permanent

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. Both permanent and determinant are special cases of a more general function of a matrix called the immanant.

Definition

The permanent of an n-by-n matrix A = (a_i,j) is defined as

The sum here extends over all elements σ of the symmetric group S_n; i.e. over all permutations of the numbers 1, 2, ..., n.

For example,

and

The definition of the permanent of A differs from that of the determinant of A in that the signatures of the permutations are not taken into account.

The permanent of a matrix A is denoted per A, perm A, or Per A, sometimes with parentheses around the argument. In his monograph, Minc (1984) uses Per(A) for the permanent of rectangular matrices, and uses per(A) when A is a square matrix. Muir (1882) uses the notation .

The word, permanent, originated with Cauchy in 1812 as “fonctions symétriques permanentes” for a related type of function, and was used by Muir (1882) in the modern, more specific, sense.

Permanent (song)

"'Permanent" is a song recorded by American rock singer David Cook. Written by Cook, Chantal Kreviazuk, and Raine Maida, its lyrics make allusions to Cook's late brother, Adam, who had battled with brain cancer before his death from this disease. The song was performed on the finale of season 8 of the TV show American Idol, and the performance then released onto iTunes as a charity single via RCA Records on May 18, 2009. It also appears on his debut studio album, David Cook (2008).

All proceeds from iTunes sales of the American Idol finale performance of the song will go to ABC² (Accelerate Brain Cancer Cure).

Commercial reception

"Permanent" debuted at number 24 on the U.S. Billboard Hot 100 chart for the chart week of May 29, 2009, and number 10 on the Digital Songs component chart, selling 103,000 downloads. It also debuted at number 26 on the Billboard Canadian Hot 100 and number 7 on the Canadian Digital Songs component chart. As of June 2009, the song has sold 159,000 units, of which 98,000 are of the version on David Cook and 61,000 are from the AI Charity Version.

Permanent (disambiguation)

Permanent is a concept in linear algebra.

Permanent may also refer to:

Art, entertainment, and media

Music

Albums

Songs

Other uses

See also

State

State may refer to:

Law and politics

Science and technology

State (magazine)

State.ie (formerly State Magazine) is an Irish website and formerly a monthly music magazine, which launched in April 2008 and ceased to print in January 2009 having published a total of ten issues. The magazine continues online and was voted Best Music Site in 2008 and Best Web Publication in 2010 in the Irish Web Awards. Originally the concept of the magazine involved a hard copy of which there was a charge to purchase, however after six issues it was decided to make the magazine's content free both online and in print. The first issue, April 2008, appeared on Irish shelves on 6 March 2008 and featured Michael Stipe of R.E.M. on the cover. This immediately garnered comparisons between the new magazine's similarities with Hot Press who featured Stipe on their cover at the same time, a move widely thought to be an attempt by Hot Press to stifle State's status as a serious 'alternative' to the more established local magazine. At a price of €5.50, State charged €2 more than Hot Press.

State (MBTA station)

State, well known as State Street, is a subway station of the Massachusetts Bay Transportation Authority. Located in downtown Boston, Massachusetts, State is the transfer point between the Orange Line and the Blue Line, as one of the quartet of "hub stations" on the MBTA subway system.

What later became the Blue Line platforms of State station were opened in 1904, making it the oldest surviving MBTA rapid transit (heavy rail) station. (The Tremont Street Subway, opened in 1897, serves only Green Line (light rail) streetcars). After an extensive renovation which was completed in 2011, State is fully handicapped accessible.

History

East Boston Tunnel

The Blue Line section of the station was built along with the rest of the East Boston Tunnel in the first years of the 20th century and opened on December 30, 1904, serving streetcars running from downtown to East Boston. An unusual aspect of State Street station is the entrance built directly into one of Boston's best-known historic sites, the Old Massachusetts State House. This entrance often confuses first-time tourists and visitors with its unconventional location. The East Boston Tunnel station was originally known as Devonshire after the street which the Old State House is located on. The station is the only remaining station on the tunnel opened in 1904.

Daylight (EP)

Daylight is an EP by American hip hop artist Aesop Rock. It was released via Definitive Jux on February 5, 2002. It is also the title of a single from his 2001 album, Labor Days. The song is included on the EP, along with a reworking entitled "Night Light."

In 2015, it was chosen by Fact as one of the 100 Best Indie Hip-Hop Records of All Time.

Track listing

References

External links