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Group theory? This solution doesn't make sense...

  1. Jul 22, 2015 #1
    Case 2:
    I get that D = c I means A must also be proportional to I but how does that mean B must be diagonal?

    Question:
    Screen Shot 2015-07-22 at 17.14.32.png
    Answers:
    Screen Shot 2015-07-22 at 17.17.04.png

    Screen Shot 2015-07-22 at 17.18.17.png

    Screen Shot 2015-07-22 at 17.18.59.png



    Screen Shot 2015-07-22 at 17.20.00.png
     
  2. jcsd
  3. Jul 22, 2015 #2

    DEvens

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    Education Advisor
    Gold Member

    It does not show that B is diagonalizable. B is presumed to be such. The point is that there is a transform that makes B diagonal and also makes A diagonal IFF A and B commute. The particular case of A proportional to the identity matrix means that A is always diagonal. Because every similarity transform on the identity matrix simply gives back the identity matrix. So, in this case, any similarity transform that makes B diagonal will leave A unchanged and still diagonal.
     
  4. Jul 25, 2015 #3
    THANKS! :D
     
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