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Math Help - Proof inner product

  1. #1
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    Proof inner product

    Let V be the vector space of m x n matrices over R. Prove that

    inner product of (A, B) = trace((B transpose)A)

    defines an inner prduct in V.
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  2. #2
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    Quote Originally Posted by Shaun Gill View Post
    Let V be the vector space of m x n matrices over R. Prove that

    inner product of (A, B) = trace((B transpose)A)

    defines an inner prduct in V.
    This is not true, under this definition the inner product can be negative
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  3. #3
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    First, an inner product can be negative. (No inner product of a vector with itself can be negative.) In fact the standard dot product is an inner product.

    This problem is an exercise in using subscripts. Compare the standard inner product on the nxn matrices with the definition of trace([B^t]A).
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