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Matrix transformation and inequality

  1. Aug 16, 2012 #1
    1. The problem statement, all variables and given/known data

    Suppose U and V are unitary matrix, A and B are positive definite,

    Does:

    UAU-1 < VBV-1

    implies A < B

    and vice versa?
     
  2. jcsd
  3. Aug 16, 2012 #2

    Ray Vickson

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    What do you mean by Y < Z for two matrices Y and Z?

    RGV
     
  4. Aug 16, 2012 #3
    A < B means that (B-A) > 0 or (B-A) is positive definite
     
  5. Aug 16, 2012 #4

    Zondrina

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    Are you referring to A and B as matricies?
     
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