Suppose we have two positive definite matrices A and B. Is it correct to claim that all the eigenvalues of A+B are greater or equal to those of A?  

Please note that:
1- I need to compare all the eigenvalues and not only the largest ones.
2- A and B are not necessarily diagonal.



Comparing eigenvalues of A+B and A where both A and B are positive definite matrices
Yes. [Weyl's inequality for matrices](http://en.wikipedia.org/wiki/Weyl%27s_inequality) shows that what you say is true.


