IsPositiveDefinite

Tests if a matrix is positive definite.

Syntax

• IsPositiveDefinite(A[, ε])

  • A is a matrix

  • ε is a positive number

Description

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

Examples

IsPositiveDefinite(HermitianSquare(RandomMatrix(5)))

true

See also

• IsPositiveSemidefinite

• IsNegativeDefinite

• IsNegativeSemidefinite

• IsIndefinite