---
tag: 0693Y2METT
kind: concept
name: Hessian matrix
aliases: [hessian]
msc: [26B05]
uses: [09ZXGX55DM]
sources:
  - url: https://en.wikipedia.org/wiki/Hessian_matrix
    locator: lead section
same_as:
  wikidata: Q620495
  wikipedia: Hessian matrix
---

## Summary

The Hessian matrix of a real-valued function of $n$ variables at a point is the $n \times n$ matrix of its second [[partial derivatives|09ZXGX55DM]] at that point.
It describes the curvature of the function, and it is the main tool of the second derivative test for local extrema.