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A matrix whose entries are polynomials.

A right eigenvector is defined as a column vector X_R satisfying AX_R=lambda_RX_R. In many common applications, only right eigenvectors (and not left eigenvectors) need be ...

Let A=a_(ij) be an n×n matrix with complex (or real) entries and eigenvalues lambda_1, lambda_2, ..., lambda_n, then sum_(i=1)^n|lambda_i|^2<=sum_(i,j=1)^n|a_(ij)|^2 (1) ...

A matrix A for which A^(H)=A^(T)^_=A, where the conjugate transpose is denoted A^(H), A^(T) is the transpose, and z^_ is the complex conjugate. If a matrix is self-adjoint, ...

The shear matrix e_(ij)^s is obtained from the identity matrix by inserting s at (i,j), e.g., e_(12)^s=[1 s 0; 0 1 0; 0 0 1]. (1) Bolt and Hobbs (1998) define a shear matrix ...

A system is singular if its condition number is infinite and ill-conditioned if it is too large.

A diagonal of a square matrix which is traversed in the "northeast" direction. "The" skew diagonal (or "secondary diagonal") of an n×n square matrix is the skew diagonal from ...

An n×n array is called a square array. Considered as a matrix, a square array is called a square matrix.

A lower triangular matrix having 0s along the diagonal as well as the upper portion, i.e., a matrix A=[a_(ij)] such that a_(ij)=0 for i<=j. Written explicitly, L=[0 0 ... 0; ...

A strictly upper triangular matrix is an upper triangular matrix having 0s along the diagonal as well as the lower portion, i.e., a matrix A=[a_(ij)] such that a_(ij)=0 for ...