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Thread: trace derivatives

  1. #1 trace derivatives 
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    Having trouble ironing out an apparent inconsistency in matrix trace derivative rules.

    Two particular rules for matrix trace derivatives are



    and



    Now assume that is diagonal (or maybe even just symmetric) and is anti-symmetric. Then by the cyclic property of the trace, . So the two derivatives should be equal up to a minus sign, no?

    However, the first rule returns the derivative



    and the second returns

    .


    Am I missing something?


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Well, if A is diagonal, then XA = AX, right?


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  4. #3  
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    Quote Originally Posted by MagiMaster View Post
    Well, if A is diagonal, then XA = AX, right?
    No, the matrices do not commute:



    but

    Last edited by em12; August 14th, 2011 at 08:23 AM.
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  5. #4  
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    Huh. Been too long since I've messed with matrices apparently.
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