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Math Help - inner product law

  1. #1
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    inner product law

    A is invertible real function,x is a vector
    on what law
    (AA^tx,x)=(A^tx,A^tx)

    ?
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  2. #2
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    Re: inner product law

    I presume you mean that A is a linear transformation- whether it is invertible is not really relevant. This is just the definition of A^T: If A is a linear transformation from vector space U to vector space V, then A^T is defined as the linear transformation from V back to U such that (Au, v)= (u, A^Tv) for any u in U and any v in V. The first inner product is in V and the second in U.

    Starting from (AA^Tx, x) with u= A^Tx and v= x that gives
    (AA^Tx, x)= (Au, v)= (u, A^Tv)= (A^Tx, A^Tx).
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  3. #3
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    Re: inner product law

    thanks
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