NegativeDefiniteMatrixQ

NegativeDefiniteMatrixQ[m] gives True if m is explicitly negative definite, and False otherwise.

Examples

Test for negative definite:

NegativeDefiniteMatrixQ[{{-2, 0}, {0, -1}}]
(* True *)

Positive definite returns false:

NegativeDefiniteMatrixQ[{{1, 0}, {0, 1}}]
(* False *)

Please visit the official Wolfram Language Reference for more details.