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

- A matrix m is positive semidefinite if Re[Conjugate[x].m.x]≥0 for all 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 λ≤t λmax are taken to be zero where λmax is an eigenvalue largest in magnitude.
- The option Tolerance has Automatic as its default value.
Examples
open allclose allSee Also
PositiveDefiniteMatrixQ NegativeDefiniteMatrixQ NegativeSemidefiniteMatrixQ HermitianMatrixQ SymmetricMatrixQ Eigenvalues SquareMatrixQ
Related Guides
Introduced in 2014
(10.0)