Matrix Predicates 

Mathematica 10 adds a number of matrix predicates, for testing matrix properties. Matrix predicates are typically used for algorithms that need to verify a property of input matrices before running the algorithm.

Symmetry-related matrix predicates.

	SymmetricMatrixQ[m]
	AntisymmetricMatrixQ[m]
	HermitianMatrixQ[m]
	AntihermitianMatrixQ[m]

Quadratic-form-related matrix predicates.

	PositiveDefiniteMatrixQ[m]	for all nonzero
	PositiveSemidefiniteMatrixQ[m]	for all nonzero
	NegativeDefiniteMatrixQ[m]	for all nonzero
	NegativeSemidefiniteMatrixQ[m]	for all nonzero
	IndefiniteMatrixQ[m]	otherwise

Inner-product-related matrix predicates.

	OrthogonalMatrixQ[m]	is identity matrix,
	UnitaryMatrixQ[m]	is identity matrix,

Eigenvalue-related matrix predicates.

	DiagonalizableMatrixQ[m]	for diagonal
	NormalMatrixQ[m]	for diagonal or