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Linear Algebra - orthogonal vector fields

  1. Sep 30, 2012 #1
    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.
     
  2. jcsd
  3. Oct 1, 2012 #2
    Still relevant. [Bringing back to 1st page, after 24 hours...]
     
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