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Math Help - [SOLVED] Symmetric Matrix Factorizations

  1. #1
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    [SOLVED] Symmetric Matrix Factorizations

    Class notes and textbook skim this topic. Most internet resources are too complex for my current level of knowledge.

    Need a little advice on how to approach the following problems.

    What I know: Symmetric Matrix <=> A^T = A

    The following statements produce a symmetric matrix assuming A^T = A, and B^T = B:

    A^2 - B^2 True
    (A - B)(A + B) False
    ABA False
    ABAB False

    Did I get these all correct?

    Therefore the product of two symmetric matrices isn't necessarily symmetric.
    What would be some conditions where they would be symmetric?
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  2. #2
    ynj
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    Quote Originally Posted by Noxide View Post
    Class notes and textbook skim this topic. Most internet resources are too complex for my current level of knowledge.

    Need a little advice on how to approach the following problems.

    What I know: Symmetric Matrix <=> A^T = A

    The following statements produce a symmetric matrix assuming A^T = A, and B^T = B:

    A^2 - B^2 True
    (A - B)(A + B) False
    ABA False
    ABAB False

    Did I get these all correct?

    Therefore the product of two symmetric matrices isn't necessarily symmetric.
    What would be some conditions where they would be symmetric?
    Not exactly.
    (ABA)^T=A^TB^TA^T=ABA
    if AB=BA,A^T=A,B^T=B, then (AB)^T=B^TA^T=BA=AB
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