# Verify a matrix is positive semi-definite

**URL:** <https://discourse.julialang.org/t/verify-a-matrix-is-positive-semi-definite/23329>\
**Category:** General Usage\
**Created:** [April 20, 2019, 2:28am UTC](https://discourse.julialang.org/t/verify-a-matrix-is-positive-semi-definite/23329 "2019-04-20T02:28:49Z")\
**Posts on this page:** 1\
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**Author:** ![Tamas\_Papp](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/tamas_papp/32/25949_2.png) [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)\
**Post date:** [April 20, 2019, 5:23am UTC](https://discourse.julialang.org/t/verify-a-matrix-is-positive-semi-definite/23329/4 "2019-04-20T05:23:25Z")

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> [@Mr.Robot](#):
>
> Then I need to verify in both directions, i.e.
> 
> 1. Given a positive semidefinite matrix A\mathbf{A}, show that it is a covariance matrix.
> 2. Given a covariance matrix, show that it is positive semidefinite.

I am not sure I understand the whole context, but this is a [well-known property](https://en.wikipedia.org/wiki/Definiteness_of_a_matrix#Connections) (covariance matrices are psd, and psd matrices are covariance matrices). I don’t know how you could verify a statement about an uncountably infinite set numerically.

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