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Matrix question

  1. Jan 22, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    What is meant by [itex]A^c[/itex] notation in matrix, where A is any arbitrary matrix?


    3. The attempt at a solution
    I've searched all over the internet and reference books that I have but none of them gives information about this thing. Please help me.
     
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  3. Jan 22, 2014 #2

    Mark44

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    Could you give us some context for this notation, such as where you saw it and some of the explanatory text? Are the entries in the matrix complex? If so, AC might mean the conjugate of A. I have never seen this notation before.
     
  4. Jan 22, 2014 #3

    utkarshakash

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    At first I also suspected that it should be conjugate. But the matrix in the original question was not complex. I had to select an option from 4 given options. If I assume the notation to be conjugate then there would be three correct options which is not possible. That's why, I'm ruling out the possibility of conjugate notation.
     
  5. Jan 22, 2014 #4

    Mark44

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    What are the four options? That might help us understand what the notation is supposed to mean. Also, check your textbook to see if they have defined this notation.
     
  6. Jan 22, 2014 #5
    It is the compliment set of A, everything not in A.
     
  7. Jan 22, 2014 #6

    haruspex

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    You mean 'complement', but A is given to be a matrix, not a set.
     
  8. Jan 23, 2014 #7

    utkarshakash

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    Here's the original question

    [itex] A = \left[ \begin{array}{cc} \cos \theta & \sin \theta \\ - \sin \theta & \cos \theta \end{array} \right] \\ B = \left[ \begin{array}{cc} \sin \theta & \cos \theta \\ - \cos \theta & \sin \theta \end{array} \right][/itex]

    Four options are

    [itex]A = B^{-1} \\ A^c = B^{-1} \\ A^c = (B^c)^{-1} \\ A^{-1} = B^c [/itex]

    Now If I suppose A^c to be conjugate of A then there is no difference between first 3 options as A^c = A, because the matrix does not contain complex variables.
     
  9. Jan 23, 2014 #8

    haruspex

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    So compute AB. can you figure out what the resulting matrix does to the plane?
     
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