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For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...

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.

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 ...

The orthogonal decomposition of a matrix into lower trapezoidal matrices.

A matrix for which horizontal and vertical dimensions are not the same (i.e., an m×n matrix with m!=n).

A p×q submatrix of an m×n matrix (with p<=m, q<=n) is a p×q matrix formed by taking a block of the entries of this size from the original matrix.

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...