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The four-dimensional version of the gradient, encountered frequently in general relativity and special relativity, is del _mu=[1/cpartial/(partialt); partial/(partialx); ...

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) ...

Green's identities are a set of three vector derivative/integral identities which can be derived starting with the vector derivative identities del ·(psidel phi)=psidel ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

Weak convergence is usually either denoted x_nw; ->x or x_n->x. A sequence {x_n} of vectors in an inner product space E is called weakly convergent to a vector in E if ...

The algebraic identity (sum_(i=1)^na_ic_i)(sum_(i=1)^nb_id_i)-(sum_(i=1)^na_id_i)(sum_(i=1)^nb_ic_i) =sum_(1<=i<j<=n)(a_ib_j-a_jb_i)(c_id_j-c_jd_i). (1) Letting c_i=a_i and ...

A Hermitian form on a vector space V over the complex field C is a function f:V×V->C such that for all u,v,w in V and all a,b in R, 1. f(au+bv,w)=af(u,w)+bf(v,w). 2. ...

A representation of a Lie algebra g is a linear transformation psi:g->M(V), where M(V) is the set of all linear transformations of a vector space V. In particular, if V=R^n, ...

The term "transition matrix" is used in a number of different contexts in mathematics. In linear algebra, it is sometimes used to mean a change of coordinates matrix. In the ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...