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Numerical Range

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data
    If T is a linear transformation on the finite-dimensional inner product space over complex numbers and is normal, then prove that the numerical range of T is convex.


    2. Relevant equations



    3. The attempt at a solution
    If we assume a and b are in the numerical range of T, then we have to prove that (1-c)a + c b is also in the numerical range of T for 0<= c <= 1. Can someone give some help, please?
     
    Last edited: May 11, 2009
  2. jcsd
  3. May 11, 2009 #2

    quasar987

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    which finite-dimensional inner product space? And what is the codomain of T?

    what does normal mean?

    Do you mean "prove that the image of T is convex"?
     
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