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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 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.

An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that x^*Ax>0>y^*Ay, where x^* denotes the conjugate transpose. A matrix m may be tested to ...

A negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive. A matrix m may be tested to determine if it is negative semidefinite in the ...

A nonpositive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a nonpositive number, i.e., a_(ij)<=0 for all i, j. Nonpositive matrices are ...

A bilinear basis is a basis, which satisfies the conditions (ax+by)·z=a(x·z)+b(y·z) z·(ax+by)=a(z·x)+b(z·y).

A group in which the elements are square matrices, the group multiplication law is matrix multiplication, and the group inverse is simply the matrix inverse. Every matrix ...