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Finding a matrix to represent a 2x2 transpose mapping

  1. Oct 27, 2015 #1
    1. The problem statement, all variables and given/known data
    Let L be a mapping such that L(A) = A^t, the transpose mapping. Find a matrix representing L with respect to the standard basis [1,1,1,1]

    2. Relevant equations


    3. The attempt at a solution
    So should I end up getting a 4x4 matrix here? I got 1,0,0,0 for the first column, 0,0,1,0 for the second column, 0,1,0,0 for the third column and 0,0,0,1 for the fourth column. is this correct?
     
  2. jcsd
  3. Oct 27, 2015 #2

    Mark44

    Staff: Mentor

    How is [1, 1, 1, 1] a basis?
    I think you mean {<1, 0, 0, 0>, <0, 1, 0, 0>, <0, 0, 1, 0>, <0, 0, 0, 1>}.
    This works, if it's legitimate to work with vectors in ##\mathbb{R}^4## instead of 2 x 2 matrices. Of course ##\mathbb{M}_{2 x 2}## is isomorphic to ##\mathbb{R}^4##. Based on what I think the problem statement is supposed to mean, your solution looks fine.
     
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