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Linear algebra proof

  1. Apr 24, 2010 #1
    1. The problem statement, all variables and given/known data
    show that if A is diagonalizable and if B is similar to A , then B is diagonalizable .

    Suppose that (S^-1)AS=D and (W^-1)AW=B

    S^-1 = S inverse
    3. The attempt at a solution

    so i solved for A and then plugged it in
    getting
    (S^-1)WB(W^-1)S=D

    so we want to get it into the form ((SW)^-1)B(SW)=D
    but i don’t know how to get there from the one above
     
  2. jcsd
  3. Apr 24, 2010 #2

    gabbagabbahey

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    Gold Member

    Not necessarily, you only need it to be in the form P-1BP=D for some P....what do you get if you let P=W-1S?:wink:
     
  4. Apr 24, 2010 #3
    oh ok , i see , thanks for your help.
     
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