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Thread: about symetric positive definite matrices

  1. #1
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    about 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
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by masterinex View Post
    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
    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.
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  3. #3
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    ohw that means A+B is positive definite aswell , but is A+B also symetric
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  4. #4
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    Well, what's $\displaystyle (A+B)^T$?
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