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Homework Help: Verify that any square matrix is a linear operator when considered as a linear map.

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data

    Verify that any square matrix is a linear operator when considered as a linear transformation.

    2. Relevant equations



    3. The attempt at a solution

    If a square matrix A[itex]\in[/itex]ℂ[itex]^{n,n}[/itex] is a linear operator on the vector space C[itex]^{n}[/itex], where n ≥ 1, then the square matrix A is of the correct dimension to be a linear transform from C->C.
     
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  3. Oct 9, 2011 #2

    HallsofIvy

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    Re: Verify that any square matrix is a linear operator when considered as a linear ma

    Except for the rather trivial statement about dimension, I see no attempt at this problem- the question is to show that it is linear.
     
  4. Oct 9, 2011 #3
    Re: Verify that any square matrix is a linear operator when considered as a linear ma

    Could I get a push in the right direction?
     
  5. Oct 9, 2011 #4

    Deveno

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    Re: Verify that any square matrix is a linear operator when considered as a linear ma

    show it preserves sums and scalar multiples....
     
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