(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

V: complex inner product space with adjoint T*

Suppose that < T( x ) , x > = 0 for all x in V, then T is the zero transformation.

3. The attempt at a solution

< T( x ) , x > = < x, T*(x ) > = 0

0 = < x, 0 > = < 0, x >

< x, T*(x ) > = 0 = < x, 0 >

if < x , y > = < x, z> , then y = z

so T*(x ) = 0 for any x, which means T* is the zero transformation, which implies that T is the zero transformation..

is this okay? thanks

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# Homework Help: Adjoint question

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