# trace inequality

Let be positive semidefinite, by Jensen's inequality, it is easy to see , whenever .

What about the , is it still valid?

## Bibliography

* indicates original appearance(s) of problem.

### this inequality is not true.

On December 20th, 2010 Anonymous says:

this inequality is not true. It was denied some years ago. See X.Z Zhan's

## clarification

I suppose that A and B are square hermitian matrixes and that s and r are real numbers. But what are the brackets supposed to represent? Sorry for my ignorance if it is obvious.