- #1

Trollfaz

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On a side note I'm posting on PF more frequently as I have exams coming and I need some help to understand some concepts. After my exams I will probably go inactive for a while.

So I'll get to the point. Suppose we have a matrix A and I wish to check if it is positive semi definite. So one easy way is to see if all it's eigenvalues are ##\ge 0##.

Another way is to test using the definition of PSD

$$v^T Av\ge 0\ v \in R^n$$

But sometimes things get really messy when I try to test a matrix with arbitrary parameters say I'm testing ##\triangledown ^2 f(x)## for PSD to check if f(x) is convex. Is there any other ways to prove for PSD in a matrix

So I'll get to the point. Suppose we have a matrix A and I wish to check if it is positive semi definite. So one easy way is to see if all it's eigenvalues are ##\ge 0##.

Another way is to test using the definition of PSD

$$v^T Av\ge 0\ v \in R^n$$

But sometimes things get really messy when I try to test a matrix with arbitrary parameters say I'm testing ##\triangledown ^2 f(x)## for PSD to check if f(x) is convex. Is there any other ways to prove for PSD in a matrix

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