Check whether a symmetric matrix is negative semi-definite, a relaxed version of negative definite that allows zero.
Check whether a symmetric matrix is negative semi-definite, a relaxed version of negative definite that allows zero.
Semi-definiteness is a looser condition than definiteness — it allows borderline zero cases, not just strictly negative ones. Correctly testing it requires checking every principal minor (not just the leading ones), confirming that all odd-order principal minors are zero or negative and all even-order ones are zero or positive.
