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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 ...

The subdiagonal of a square matrix is the set of elements directly under the elements comprising the diagonal. For example, in the following matrix, the diagonal elements are ...

The superdiagonal of a square matrix is the set of elements directly above the elements comprising the diagonal. For example, in the following matrix, the diagonal elements ...

Sylvester's criterion states that a matrix M is positive definite iff the determinants associated with all upper-left submatrices of M are positive.