From 8c7dc9c58139c7509c9411df02d143a3c8d21d3f Mon Sep 17 00:00:00 2001 From: RituPande Date: Mon, 2 Sep 2024 16:49:59 -0400 Subject: [PATCH] Update 2024-07-24-Simultaneous-Matrix-Diagonalization.md --- _posts/2024-07-24-Simultaneous-Matrix-Diagonalization.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/_posts/2024-07-24-Simultaneous-Matrix-Diagonalization.md b/_posts/2024-07-24-Simultaneous-Matrix-Diagonalization.md index fdfd66660b0b8..77bbc3fcdbe2c 100644 --- a/_posts/2024-07-24-Simultaneous-Matrix-Diagonalization.md +++ b/_posts/2024-07-24-Simultaneous-Matrix-Diagonalization.md @@ -16,5 +16,8 @@ published: false - C_ab = C_a * C_b - C_a C_b = C_b C_a +Schur's Lemma +- The only relationship that can exist between who irredicuble repressentation is similarity + XR=R'X i.e. $$XRX^{-1} = R'$$ - If a matrix X commutes with all the matrices of a collection of irreducible matrices, i.e XR = RX, for all R's in the collection then it has to be a scalar multiple if identity matix I