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An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...

A decomposition of a module into a direct sum of submodules. The index set for the collection of submodules is then called the grading set. Graded modules arise naturally in ...

A polynomial with matrix coefficients. An nth order matrix polynomial in a variable t is given by P(t)=A_0+A_1t+A_2t^2+...+A_nt^n, where A_k are p×p square matrices.

The bandwidth of a matrix M=(m_(ij)) is the maximum value of |i-j| such that m_(ij) is nonzero.

A matrix whose eigenvectors are not complete.

The index set for the collection of submodules in a graded module.

A square matrix which is not reducible is said to be irreducible.

The (n+1)×(n+1) tridiagonal matrix (also called the Clement matrix) defined by S_n=[0 n 0 0 ... 0; 1 0 n-1 0 ... 0; 0 2 0 n-2 ... 0; | | ... ... ... |; 0 0 0 n-1 0 1; 0 0 0 0 ...

A pair of matrices ND^(-1) or D^(-1)N, where N is the matrix numerator and D is the denominator.

A set M of all polynomials in s variables, x_1, ..., x_s such that if P, P_1, and P_2 are members, then so are P_1+P_2 and QP, where Q is any polynomial in x_1, ..., x_s.