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Determine whether the function is a linear transformation (Attempt inside)

  1. Nov 7, 2011 #1
    T: Mnn => R, where T(A) = tr(A)

    Attempt:

    1) T(kA) = tr(kA) = k tr(A) = k T(A)



    2) T(A+B) = tr (A + B) = tr(A) + tr(B) = T(A) + T(B)

    so it's linear transformation. Am I correct?
     
  2. jcsd
  3. Nov 7, 2011 #2

    Deveno

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    Science Advisor

    technically, yes, but if that was homework, and i were grading it, i don't think i'd give it full marks.

    you should show a little more work, you haven't used the definition of trace anywhere...
     
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