# What is the fastest way to check if a hermitian matrix is positive semi-definite?

**URL:** <https://discourse.julialang.org/t/what-is-the-fastest-way-to-check-if-a-hermitian-matrix-is-positive-semi-definite/110769>\
**Category:** Performance\
**Tags:** linearalgebra\
**Created:** [February 26, 2024, 11:14am UTC](https://discourse.julialang.org/t/what-is-the-fastest-way-to-check-if-a-hermitian-matrix-is-positive-semi-definite/110769 "2024-02-26T11:14:34Z")\
**Posts on this page:** 1\
**Showing post:** 2

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**Author:** ![gdalle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gdalle/32/27854_2.png) [@gdalle](https://discourse.julialang.org/u/gdalle)\
**Post date:** [February 26, 2024, 11:23am UTC](https://discourse.julialang.org/t/what-is-the-fastest-way-to-check-if-a-hermitian-matrix-is-positive-semi-definite/110769/2 "2024-02-26T11:23:09Z")

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This is probably related (replace largest with smallest):

> [@Efficient computation of largest eigenvalue](https://discourse.julialang.org/t/efficient-computation-of-largest-eigenvalue/105933):
>
> For some numerical simulations I run, I need to construct a matrix and obtain its leading eigenvalue. I will make use of both of them. I was using the LinearAlgebra package, and computing the leading eigenvalue as maximum(real(eigvals(matrix))). When profiling the code, I noticed that this computation takes a noticeable amount of time, especially for larger matrices, so I am trying to speed it up. I cannot use eigvals! because I need the matrix later and do not want to override it. Furthermore…

As a side note, for small arrays, you should get a significant speedup with StaticArrays.jl

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