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Vector subtraction is the process of taking a vector difference, and is the inverse operation to vector addition.

For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

A perfect ruler also called a complete ruler, is type of ruler considered by Guy (1994) which has k distinct marks spaced such that the distances between marks can be used to ...

An operator A^~ is said to be antiunitary if it satisfies: <A^~f_1|A^~f_2> = <f_1|f_2>^_ (1) A^~[f_1(x)+f_2(x)] = A^~f_1(x)+A^~f_2(x) (2) A^~cf(x) = c^_A^~f(x), (3) where ...

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

An operator U satisfying U^|U = 1 (1) UU^| = 1, (2) where U^| is the adjoint.

For operators A^~ and B^~, the anticommutator is defined by {A^~,B^~}=A^~B^~+B^~A^~.

The antilaplacian of u with respect to x is a function whose Laplacian with respect to x equals u. The antilaplacian is never unique.

A quantity which changes sign when indices are reversed. For example, A_(ij)=a_i-a_j is antisymmetric since A_(ij)=-A_(ji).

The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...