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Scalar multiplication refers to the multiplication of a vector by a constant s, producing a vector in the same (for s>0) or opposite (for s<0) direction but of different ...

Let A and B be two *-algebras. An algebraic homomorphism phi:A->B is called *-homomorphism if it satisfies phi(a^*)=phi(a)^* for each a in A.

A tensor category (C, tensor ,I,a,r,l) is strict if the maps a, l, and r are always identities. A related notion is that of a tensor R-category.

The subdiagonal of a square matrix is the set of elements directly under the elements comprising the diagonal. For example, in the following matrix, the diagonal elements are ...

An R-module M is said to be unital if R is a commutative ring with multiplicative identity 1=1_R and if 1m=m for all elements m in M.

A vector difference is the result of subtracting one vector from another. A vector difference is denoted using the normal minus sign, i.e., the vector difference of vectors A ...

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 ...

A function of one or more variables whose range is three-dimensional (or, in general, n-dimensional), as compared to a scalar function, whose range is one-dimensional. Vector ...

The following vector integrals are related to the curl theorem. If F=cxP(x,y,z), (1) then int_CdsxP=int_S(daxdel )xP. (2) If F=cF, (3) then int_CFds=int_Sdaxdel F. (4) The ...

Let theta be the angle between two vectors. If 0<theta<pi, the vectors are positively oriented. If pi<theta<2pi, the vectors are negatively oriented. Two vectors in the plane ...