Recent content by Sepen

  1. S

    Is the Image of a Normal Operator the Same as Its Adjoint?

    Ah it would be Im(T) and it would be Im(T*) so thus they have to be equal?
  2. S

    Is the Image of a Normal Operator the Same as Its Adjoint?

    I understand that but does that necessarily imply that they have to be equal? I recognize that they have to have the same dimensions in that case, but that doesn't get me anywhere.
  3. S

    Is the Image of a Normal Operator the Same as Its Adjoint?

    Is that necessarily true? And if it is (I know that you can show that Im(T) is orthogonal to Ker(T*) and vice versa), but how does that specifically help?
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    Is the Image of a Normal Operator the Same as Its Adjoint?

    Homework Statement Show that if T is a normal operator on a finite dimensional vector space than it has the same image as its adjoint. Homework Equations N/A The Attempt at a Solution I have been able to show that both T and T^{*} have the same kernel. Thus, by using the finite...