- published: 09 Aug 2008
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In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number obtained by multiplying corresponding entries and then summing those products. The name "dot product" is derived from the centered dot " Failed to parse (Missing texvc executable; please see math/README to configure.): \cdot " that is often used to designate this operation; the alternative name "scalar product" emphasizes the scalar (rather than vector) nature of the result.
When two Euclidean vectors are expressed in terms of coordinate vectors on an orthonormal basis, the inner product of the former is equal to the dot product of the latter. For more general vector spaces, while both the inner and the dot product can be defined in different contexts (for instance with complex numbers as scalars) their definitions in these contexts may not coincide.
In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result. The dot product is directly related to the cosine of the angle between two vectors in Euclidean space of any number of dimensions.