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

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- Dec 8th 2009, 12:40 PMmasterinexabout symetric positive definite matrices
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 - Dec 8th 2009, 12:50 PMTheEmptySet
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.(Rock) - Dec 8th 2009, 01:11 PMmasterinex
ohw that means A+B is positive definite aswell , but is A+B also symetric É

- Dec 8th 2009, 01:18 PMDefunkt
Well, what's $\displaystyle (A+B)^T$?