---
tag: 01MMVW8CKC
kind: concept
name: Positive semidefinite matrix
msc: [15B57, 15A63]
specializes: [0P17NGQQMQ]
sources:
  - url: https://en.wikipedia.org/wiki/Definite_matrix
    locator: Definitions
inventory: [8XQP955FKQ]
---

## Summary

A positive semidefinite matrix is a Hermitian matrix $A$ with $x^* A x \ge 0$ for every vector $x$.