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Take K a number field and m a divisor of K. A congruence subgroup H is defined as a subgroup of the group of all fractional ideals relative prime to m (I_K^m) that contains ...

The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

In general, there is no unique matrix solution A to the matrix equation y=Ax. Even in the case of y parallel to x, there are still multiple matrices that perform this ...

In the Minkowski space of special relativity, a four-vector is a four-element vector x^mu=(x^0,x^1,x^2,x^3) that transforms under a Lorentz transformation like the position ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

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 ...

Let s(x,y,z) and t(x,y,z) be differentiable scalar functions defined at all points on a surface S. In computer graphics, the functions s and t often represent texture ...

A complex vector bundle is a vector bundle pi:E->M whose fiber bundles pi^(-1)(m) are a copy of C^k. pi is a holomorphic vector bundle if it is a holomorphic map between ...

A vector v on a Hilbert space H is said to be cyclic if there exists some bounded linear operator T on H so that the set of orbits {T^iv}_(i=0)^infty={v,Tv,T^2v,...} is dense ...

The partial differential equation del ^2A=-del xE, where del ^2 is the vector Laplacian.