IsPositiveSemiDefinite

Tests if a matrix is positive semidefinite.

Syntax

• IsPositiveSemidefinite(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

If A is a matrix, then IsPositiveSemidefinite(A, ε) returns true iff A is a positive semidefinite Hermitian (real case: symmetric) matrix. Floating-point numbers are compared with epsilon ε; if omitted, a default (but positive) value is used.

Examples

IsPositiveSemidefinite(HermitianSquare(RandomMatrix(5)))

true

See also

• IsPositiveDefinite

• IsNegativeDefinite

• IsNegativeSemidefinite

• IsIndefinite