# Positive operator?

1. May 31, 2005

### Seckin Sefi

"A positive operator A is defined to be an operator such that for any vector |v>=!0, <v|A|v> is real, non-negative number."

Can somebody tell me how can I check if a matrice (for example 4x4) is positive or not?

Thanks in advance

2. May 31, 2005

### matt grime

This behaviour also comes under "positive definite", ie A defines a positive definite bilinear map. Google along those lines, it's well documented,

One criterion is if the eigenvalues are all positive.

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