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Very quick matrix question

  1. Apr 3, 2012 #1
    Very quick question.

    Im 99% sure that the transpose of a matrix of only diagonal ones is always equal to its original state.

    Ie
    |1000| |1000| T
    |0100| |0100|
    |0010| = |0010|
    |0001| |0001|


    So my question is am i correct ?

    Thanks in advance.
     
  2. jcsd
  3. Apr 3, 2012 #2

    tiny-tim

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    hi mikedamike! :smile:
    yes, and it works for any diagonal matrix …

    (a)Tii = (a)ii :wink:
     
  4. Apr 3, 2012 #3

    HallsofIvy

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    The definition of "transpose" is that if the elements of A are "[itex]a_{ij}[/itex]" then the elements of A^T are [itex]a_{ji}[/itex]. So if all non-diagonal elements are 0, we have [itex]a_{ij}= a_{ji}= 0[/itex]. And, of course, on the diagonal i= j so we still have [itex]a_{ij}= a_{ji}[/itex].
     
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