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

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Basic Examples  (1)

Test if a matrix is explicitly positive semidefinite:

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This means that the quadratic form for all vectors :

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Scope  (6)

Options  (1)

Applications  (4)

Properties & Relations  (11)

Possible Issues  (2)

See Also

PositiveDefiniteMatrixQ  NegativeDefiniteMatrixQ  NegativeSemidefiniteMatrixQ  HermitianMatrixQ  SymmetricMatrixQ  Eigenvalues  SquareMatrixQ

Introduced in 2014
(10.0)