PositiveSemidefiniteMatrixQ

PositiveSemidefiniteMatrixQ[m]
gives True if m is explicitly positive semidefinite, and False otherwise.

Details and OptionsDetails and Options

  • A matrix m is positive semidefinite if Conjugate[x].m.x0 for all nonzero vectors x.
  • PositiveSemidefiniteMatrixQ works for symbolic as well as numerical matrices.
  • For approximate matrices, the option Tolerance->t can be used to indicate that all eigenvalues λ satisfying are taken to be zero where is an eigenvalue largest in magnitude.
  • The option Tolerance has Automatic as its default value.
Introduced in 2014
(10.0)