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Math Help - vector space inner product proof

  1. #1
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    vector space inner product proof

    let V be the vector space of m x n matrices over R. prove that :
    phi(A,B) = trace((transpose(B))*A)
    defines an inner product in V.
    cant work out where to start here. any pointers in the right direction would be appreciated.
    thanks
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  2. #2
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    This problem is just an exercise in notation usage. Without TeX it is next to impossible to display. However, here is a bit of guidance.
    This idea is to show that this inner product is equivalent to the usual inner product defined on the space nxn matrices. I will give a good reference Linear Algebra by Larry Smith. He shows how to work this out for <A,B>=tr{AB^T}. But his work is easily modified to this problem.
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