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Check whether a symmetric matrix is negative definite — the mirror image of positive definite.

How It Works

How Negative Definite Matrix Checker Works

A symmetric matrix is negative definite exactly when its negation is positive definite, which translates to the leading principal minors alternating in sign, starting negative (the 1×1 minor negative, the 2×2 minor positive, the 3×3 minor negative, and so on). The calculator computes each leading minor and checks this pattern.

FAQ

Frequently Asked Questions

How does this relate to positive definite?
A matrix A is negative definite exactly when −A is positive definite — the two properties are mirror images of each other.
What does negative definiteness tell you in optimization?
A negative definite Hessian at a critical point confirms you've found a local maximum, the mirror case of how a positive definite Hessian confirms a local minimum.