Suppose V is an inner product sapce

and T:V-->V

Show that dim(Im(T)) = dim(Im(T*))

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- Mar 26th 2013, 01:20 AMdave52Suppose V is an inner product..
Suppose V is an inner product sapce

and T:V-->V

Show that dim(Im(T)) = dim(Im(T*)) - Mar 26th 2013, 04:01 AMHallsofIvyRe: Suppose V is an inner product..
You mean "Suppose V is an inner product

**space**". Now, what is the**definition**of T*? - Mar 26th 2013, 04:16 AMdave52Re: Suppose V is an inner product..
T* satisfies the equation <T(v),w> = <v,T*(w)> for all v,w in V?

- Mar 26th 2013, 04:32 AMdave52Re: Suppose V is an inner product..
Thanks.

- Mar 26th 2013, 05:25 AMHallsofIvyRe: Suppose V is an inner product..
- Mar 26th 2013, 05:43 AMdave52Re: Suppose V is an inner product..
linear independent property: for all a

_{1},....,a_{n}∈ R if a_{1}v_{1}+.......+a_{n}v_{n }= 0

spanning property: for every x in Im(T*) such that x = a_{1}v_{1}+.....+a_{n}v_{n}