# \`isposdef\` inconsistent results, numerically unstable?

**URL:** https://discourse.julialang.org/t/isposdef-inconsistent-results-numerically-unstable/9013
**Category:** Numerics
**Tags:** bug
**Created:** [February 12, 2018, 1:49pm UTC](https://discourse.julialang.org/t/isposdef-inconsistent-results-numerically-unstable/9013 "2018-02-12T13:49:00Z")
**Posts on this page:** 1
**Showing post:** 10

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### Author: ![andreasnoack](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/andreasnoack/32/27_2.png) [@andreasnoack](https://discourse.julialang.org/u/andreasnoack)
#### Post date: [February 12, 2018, 3:01pm UTC](https://discourse.julialang.org/t/isposdef-inconsistent-results-numerically-unstable/9013/10 "2018-02-12T15:01:08Z")

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Our definition of positive definiteness in `isposdef` is symmetric (Hermitian) and “can be Cholesky factorized” which is pretty close to having positive eigenvalues but not as robust. We have had some discussions about using a tolerance for the symmetry check but we concluded that it was better to make the users enforce symmetry via the `Symmetric` wrapper instead of coming up with a possibly arbitrary tolerance for symmetry. Hence, as long as you keep your matrix wrapped in the `Symmetric` type, a small permutation shouldn’t change the result of `isposdef` unless the matrix is almost singular.

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