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The successive overrelaxation method (SOR) is a method of solving a linear system of equations Ax=b derived by extrapolating the Gauss-Seidel method. This extrapolation takes ...

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

A G-space is a special type of T1-Space. Consider a point x and a homeomorphism of an open neighborhood V of x onto an open set of R^n. Then a space is a G-space if, for any ...

A linear transformation A:R^n->R^n is hyperbolic if none of its eigenvalues has modulus 1. This means that R^n can be written as a direct sum of two A-invariant subspaces E^s ...

A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...

A polynomial function is a function whose values can be expressed in terms of a defining polynomial. A polynomial function of maximum degree 0 is said to be a constant ...

The vector space generated by the columns of a matrix viewed as vectors. The column space of an n×m matrix A with real entries is a subspace generated by m elements of R^n, ...

A generalized eigenvector for an n×n matrix A is a vector v for which (A-lambdaI)^kv=0 for some positive integer k in Z^+. Here, I denotes the n×n identity matrix. The ...

There are at least two distinct (though related) notions of the term Hilbert algebra in functional analysis. In some literature, a linear manifold A of a (not necessarily ...

The commutator series of a Lie algebra g, sometimes called the derived series, is the sequence of subalgebras recursively defined by g^(k+1)=[g^k,g^k], (1) with g^0=g. The ...