Hi , I have some question
about the properties of symmetric positive defifnte matrices.
If A and B are symmetric positive defifnte matrices , then is A+B also a symetric positive definite matrix É
A matrix $\displaystyle M$ is positive definite if for all $\displaystyle v \in V$
$\displaystyle v^TMv > 0$
So lets write it out
$\displaystyle v^T(A+B)v=(v^TA+V^TB)v=v^TAv+v^TBv$
Since both $\displaystyle A,B$ are positive difinite the above sum is positive so we are done.