The IsMatrixShape command verifies whether the matrix A is a certain "shape".

The only types of "shapes" that the IsMatrixShape command can verify are:

Diagonal : shape = diagonal

Strictly diagonally dominant : shape = strictlydiagonallydominant

Diagonally dominant : shape = diagonallydominant

Hermitian : shape = hermitian

Positive definite : shape = positivedefinite

Symmetric : shape = symmetric

Upper or lower triangular : shape = triangular[upper] or shape = triangular[lower], repectively

Tridiagonal : shape = tridiagonal

If neither upper nor lower is specified, the triangular option defaults to triangular[upper].

The Student[NumericalAnalysis] subpackage's definition of positive definiteness is as follows.

A complex n-by-n matrix A is positive definite if and only if A is Hermitian and for all n-dimensional complex vectors v, we have , where  denotes the real part of a complex number.

A real n-by-n matrix A is positive definite if and only if A is symmetric and for all n-dimensional real vectors v, we have .

To check another "shape" that is not available with the Student[NumericalAnalysis][IsMatrixShape] command see the general IsMatrixShape command.