Let Σ be a symmetric positive definite matrix with ones on the diagonal (= correlation matrix).Let A be an invertible matrix.I'm pretty sure that if Ω := A Σ A t has ones on its diagonal, then Ω = I d or Ω = Σ(which would correspond to A = I d or A = c h o l ( Σ ))But I don't know how to proove it.

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Let   Σ be a symmetric positive definite matrix with ones on the diagonal (= correlation matrix).Let   A be an invertible matrix.I&#039;m pretty sure that if   Ω  :=  A  Σ      A    t   has ones on its diagonal, then  Ω  =  I  d        or        Ω  =  Σ(which would correspond to   A  =  I  d or   A  =  c  h  o  l  (  Σ  ))But I don&#039;t know how to proove it.

Braxton Gallagher · Accepted Answer

try out some   3  ×  3 examples. In particular I suggest   Σ  =      [                            1                                      1            2                                    0                                                  1            2                                    1                          0                                      0                          0                          1                      ]    and select   A to be a permutation matrix (there are   3  !  =  6 total for you to try but you can skip   A  =  I as the result is immediate)

Let <mi mathvariant="normal">Σ be a symmetric positive definite matrix with o

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