In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:
Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors. Alternatively, it is defined as the product of the projection of the first vector onto the second vector and the magnitude of the second vector. Thus,
Cross product – also known as the "vector product", a binary operation on two vectors that results in another vector. The cross product of two vectors in 3-space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle between the two vectors. So, if is the unit vector perpendicular to the plane determined by vectors and ,
Exterior product or wedge product – a binary operation on two vectors that results in a bivector. In Euclidean 3-space, the wedge product has the same magnitude as the cross product (the area of the parallelogram formed by sides and ) but generalizes to arbitrary affine spaces and products between more than two vectors.
Tensor product – for two vectors and where and are vector spaces, their tensor product belongs to the tensor product of the vector spaces.
Geometric product or Clifford product – for two vectors, the geometric product is a mixed quantity consisting of a scalar plus a bivector. The geometric product is well defined for any multivectors as arguments.
A bilinear product in an algebra over a field.
A Lie bracket for vectors in a Lie algebra.
Hadamard product – entrywise or elementwise product of tuples of scalar coordinates, where .
Outer product - where with results in a matrix.
Triple products – products involving three vectors.
Quadruple products – products involving four vectors.
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In mathematics, vectormultiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:...
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number of uses, including Multiplication of two numbers, where it is read as "times" or "multiplied by" Cross product of two vectors, where it is usually read...
operations of multiplication and addition and scalar multiplication by elements of a field and satisfying the axioms implied by "vector space" and "bilinear"...
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complex conjugate vector space is the same underlying real vector space (same set of points, same vector addition and real scalar multiplication) with the conjugate...
scalar multiplication are trivial. A basis for this vector space is the empty set, so that {0} is the 0-dimensional vector space over F. Every vector space...
matrix multiplication. Given a field K {\displaystyle K} of either real or complex numbers, let K m × n {\displaystyle K^{m\times n}} be the K-vector space...
Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms...
include 2-d and 3-d image types.: 10–11 The following is a matrix–vectormultiplication algorithm in OpenCL C. // Multiplies A*x, leaving the result in...
element of the vector space π−1({x}). With the pointwise addition and scalar multiplication of sections, F(U) becomes itself a real vector space. The collection...
(in analogy to the way that multiplication distributes over addition). Vector spaces endowed with an additional multiplicative structure are called algebras...
between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used...
the space of column vectors can be represented as the left-multiplication of a unique row vector. To simplify writing column vectors in-line with other...
addition and scalar multiplication) are also continuous functions. Such a topology is called a vector topology and every topological vector space has a uniform...
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