---
tag: 0KX66CZMBB
kind: concept
name: Positive definite matrix
msc: [15B57, 15A63]
sources:
  - url: https://en.wikipedia.org/wiki/Definite_matrix
    locator: Definitions
---

## Summary

A positive definite matrix is a Hermitian matrix $A$ with $x^* A x > 0$ for every nonzero vector $x$.