Conjugate Transpose Inner Product Help

kolada41 · #1 $Old$ November 5th, 2009, 06:00 PM

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

tonio · #2 $Old$ November 7th, 2009, 05:34 AM

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