Numerical Range

  • #1

Homework Statement


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.


Homework Equations





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?
 
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Answers and Replies

  • #2
quasar987
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Homework Statement


If T is a linear transformation on the finite-dimensional inner product space over complex numbers
which finite-dimensional inner product space? And what is the codomain of T?

and is normal,
what does normal mean?

then prove that the numerical range of T is convex.
Do you mean "prove that the image of T is convex"?
 

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