Let <mi mathvariant="normal">&#x03A3;<!-- Σ --> be a symmetric positive definite matrix with o

Jaylene Duarte

Jaylene Duarte

Answered question

2022-05-15

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.

Answer & Explanation

Braxton Gallagher

Braxton Gallagher

Beginner2022-05-16Added 21 answers

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)

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