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Math Help - 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 M is positive definite if for all v \in V

    v^TMv > 0

    So lets write it out

    v^T(A+B)v=(v^TA+V^TB)v=v^TAv+v^TBv

    Since both 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 (A+B)^T?
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