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Vector into a diagonal Matrix

  1. Aug 1, 2011 #1
    I think this is a pretty simple question. I need a transformation that will take a Column vector e.g.: <a,b,c> and turn it into a 3x3 matrix where a is in position 1,1 and b in position 2,2 and c in position 3,3. i.e.: a diagonal matrix.

    Any help?
     
  2. jcsd
  3. Aug 1, 2011 #2

    Fredrik

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    What kind of transformation? You can define the function by saying that for each i,j we define [itex]X_{ij}=\delta_{ij}x_i[/itex]. (There's no summation over the repeated indices). Do you need to define the function by matrix multiplication alone, or is it OK to use addition too?
     
  4. Aug 2, 2011 #3

    I like Serena

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    You could pick a 3 dimensional matrix (a 3x3x3 cube) with 1's on the main diagonal.
     
  5. Aug 4, 2011 #4
    There is a linear isomorphism [itex] \alpha [/itex] such that for any vector [itex] (a, b, c) [/itex] [itex] \alpha [/itex] will take [itex] (a,b,c) [/itex] to the 3 by 3 matrix, whose main-diagonal entries are a, b, and c, with all other entries being 0.
     
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