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In the biconjugate gradient method, the residual vector r^((i)) can be regarded as the product of r^((0)) and an ith degree polynomial in A, i.e., r^((i))=P_i(A)r^((0)). (1) ...

The upside-down capital delta symbol del , also called "nabla" used to denote the gradient and other vector derivatives. The following table summarizes the names and ...

The upside-down capital delta symbol del , also called "del," used to denote the gradient and other vector derivatives. The following table summarizes the names and notations ...

A basis for the real numbers R, considered as a vector space over the rationals Q, i.e., a set of real numbers {U_alpha} such that every real number beta has a unique ...

A solenoidal vector field satisfies del ·B=0 (1) for every vector B, where del ·B is the divergence. If this condition is satisfied, there exists a vector A, known as the ...

Let M be a regular surface with v_(p),w_(p) points in the tangent space M_(p) of M. For M in R^3, the second fundamental form is the symmetric bilinear form on the tangent ...

A bounded linear operator T in B(H) on a Hilbert space H is said to be cyclic if there exists some vector v in H for which the set of orbits ...

The vector triple product identity Ax(BxC)=B(A·C)-C(A·B). This identity can be generalized to n dimensions,

A change of coordinates matrix, also called a transition matrix, specifies the transformation from one vector basis to another under a change of basis. For example, if ...

A short exact sequence of groups A, B, and C is given by two maps alpha:A->B and beta:B->C and is written 0->A->B->C->0. (1) Because it is an exact sequence, alpha is ...