# about symetric positive definite matrices

• Dec 8th 2009, 12:40 PM
masterinex
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 PM
TheEmptySet
Quote:

Originally Posted by masterinex
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.(Rock)
• Dec 8th 2009, 01:11 PM
masterinex
ohw that means A+B is positive definite aswell , but is A+B also symetric É
• Dec 8th 2009, 01:18 PM
Defunkt
Well, what's $\displaystyle (A+B)^T$?