Basic

MatrixQ   ▪ SquareMatrixQ   ▪ DiagonalMatrixQ   ▪ UpperTriangularMatrixQ   ▪ LowerTriangularMatrixQ

Symmetry Related

SymmetricMatrixQ   ▪ AntisymmetricMatrixQ   ▪ HermitianMatrixQ   ▪ AntihermitianMatrixQ

Quadratic-Form Related

PositiveDefiniteMatrixQ   ▪ NegativeDefiniteMatrixQ   ▪ PositiveSemidefiniteMatrixQ   ▪ NegativeSemidefiniteMatrixQ   ▪ IndefiniteMatrixQ

Eigenvalue Related

NormalMatrixQ   ▪ DiagonalizableMatrixQ

Inner-Product Related

OrthogonalMatrixQ   ▪ UnitaryMatrixQ

Options for Matrix Predicates

Tolerance   ▪ SameTest   ▪ Normalized