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Math Help - Conjugate Transpose Inner Product Help

  1. #1
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    Conjugate Transpose Inner Product Help

    Hi! the problem reads:

    Let V = Fn and let A in Mnxn(F)

    a) Prove that <x,Ay> = <A*x,y> for all x,y in V

    b) Suppose that for some B in Mnxn(F), we have <x,Ay>=<Bx,y> for all x,y in V. Prove that B=A*


    Thank you
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  2. #2
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    Quote Originally Posted by kolada41 View Post
    Hi! the problem reads:

    Let V = Fn and let A in Mnxn(F)

    a) Prove that <x,Ay> = <A*x,y> for all x,y in V

    b) Suppose that for some B in Mnxn(F), we have <x,Ay>=<Bx,y> for all x,y in V. Prove that B=A*


    Thank you

    What you wrote above is the very definition of conjugate A* of A that I know, so you must be using other definition...perhaps the one that says that A* is the complex conjugate transpose of A , or which one?

    Tonio
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