Linear Algebra - orthogonal vector fields

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I want to prove that: [itex]Ker(T*)=[Im(T)]^\bot[/itex]
Everything is in finite dimensions.

What I'm trying:
Let v be some vector in ImT, so there is v' so that Tv'=v.
Let u be some vector in KerT*, so T*u=0.

So now:
<u,v>=<u,Tv'>=<T*u,v'>=0 so every vector in ImT is perpendicular to every vector in KerT*.
So [itex]Ker(T*)=[Im(T)]^\bot[/itex]

My intuition tells me that there is something wrong here but I can' put a finger on it.
 

Answers and Replies

  • #2
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Still relevant. [Bringing back to 1st page, after 24 hours...]
 

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