PositiveDefiniteMatrixQ
PositiveDefiniteMatrixQ[m] gives True if m is explicitly positive definite, and False otherwise.
Examples
Test for positive definite:
PositiveDefiniteMatrixQ[{{2, -1}, {-1, 2}}]
(* True *)Not positive definite:
PositiveDefiniteMatrixQ[{{1, 2}, {2, 1}}]
(* False *)Please visit the official Wolfram Language Reference for more details.