A positive semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonnegative. A matrix m may be tested to determine if it is positive semidefinite in the Wolfram Language using PositiveSemidefiniteMatrixQ[m].

negative definite matrix | negative semidefinite matrix | positive definite matrix | positive eigenvalued matrix | positive matrix

PositiveSemidefiniteMatrixQ