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Find a matrix S1 that satisfies A= S(uppercase lamda)S^(-1)

  1. May 10, 2012 #1
    1. The problem statement, all variables and given/known data
    A matrix S and a matrix A are given. Let A = S(uppercase lamda)S-1, but do not calculate A. Find different S1 and (Uppercase lamda)1 such that the same A satisfies A = S1(Uppercase lamda)1S1-1


    2. Relevant equations



    3. The attempt at a solution
    I have given the original matrices and my work on my attachment so see that for my work. What I want to know is what exactly is S1 and (Uppercase lamda)1 and how do I solve for them?
     

    Attached Files:

  2. jcsd
  3. May 10, 2012 #2
    Your problem description doesn't make sense. I'm guessing you're given S and Lambda, not S and A.

    You should multiply both sides of equation [itex] A = S \Lambda S^{-1} [/itex] with 1 a couple of times, only write it as [itex] 1 = S_1 S_1^{-1} [/itex].
     
  4. May 11, 2012 #3
    Yak they gave me uppercase lamda and S what I am confused on is how to find S1.
     
  5. May 12, 2012 #4

    sharks

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    Gold Member

    As suggested by clamtrox, just multiply both sides by the 3x3 unit vector.
     
  6. May 12, 2012 #5
    I am confused if I do that I just get the same matrix again and I cant calculate A so what do I do?
     
  7. May 12, 2012 #6
    Of course you get the same matrix, that's the entire point. You want it to remain equal to A, but you want to write it in a different way.
     
  8. May 12, 2012 #7
    ok I think I got it
     
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