Suppose $A$, $B$ are $n ×n$ positive definite matrices and I be the $n ×n$ identity matrix. Then which of the following are positive definite?
- $ABA $
My thoughts: From the given condtion we have that the eigenvalues of $A$ and $B$ are positive and then I need to find the eigenvalues of given matrices. But how can I find them? Please help. Thanks.