# Math Help - Conjugate Transpose Inner Product Help

1. ## Conjugate Transpose Inner Product Help

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

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