A Finding Eigenvectors for Two Matrices using the Generalized Jacobi Method

hoshangmustafa
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If I have two matrices A and B, how can I find an eigenvector for the two matrices?
If I have two matrices A and B, how can I find an eigenvector for the two matrices?
 
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Eigenvectors belong to a matrix. Matrix A has its eigenvectors. Matrix B has its eigenvectors.
 
Hi,
I meant simultaneous diagonalization of two matrices.
 
I do not think simultaneously diagonalizable matters in procedure of getting eigenvectors of A and B for each.

As examples in QM, x coordinate operator X and y coordinate operator Y are simultaneously diagonarizable.
XY=YX
X has eigenvectors of {|x>}. Y has eigenvectors of {|y>}.

XX^2=X^2X
X^2 has denenerated eigenbectors of |x> and |-x> for eigenvalue x^2
 
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Hi,
for example

K=2,1;1,2
M=2,0;0,0
use the generalized Jacobi method to calculate the eigensystem problem
KΦ=λMΦ
 
As KM \neq MK, I am afraid that we cannot simultaneously diagonalize them. I might be wrong due to scarce knowledge on Jacobi method.
 
K=1,-1;-1,1
M=2,1;1,2
 
Then KM=MK. M=K+2I where I is identity matrix. Diagonalization of K by product of unitary matrix ##P, P^{-1}## would also diagonalize M. Why don't you try to get it ?
 
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