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A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement a×b=c would be read "a times b equals c," where a is called ...

The vector triple product identity is also known as the BAC-CAB identity, and can be written in the form Ax(BxC) = B(A·C)-C(A·B) (1) (AxB)xC = -Cx(AxB) (2) = -A(B·C)+B(A·C). ...

Given vectors u and v, the vector direct product, also known as a dyadic, is uv=u tensor v^(T), where tensor is the Kronecker product and v^(T) is the matrix transpose. For ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

Although the multiplication of one vector by another is not uniquely defined (cf. scalar multiplication, which is multiplication of a vector by a scalar), several types of ...

A Hermitian inner product space is a complex vector space with a Hermitian inner product.

There are a number of algebraic identities involving sets of four vectors. An identity known as Lagrange's identity is given by (AxB)·(CxD)=(A·C)(B·D)-(A·D)(B·C) (1) ...

An inner product space is a vector space together with an inner product on it. If the inner product defines a complete metric, then the inner product space is called a ...

The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...