# Simultaneous diagonalization of two matrices

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JYOTHI R on 7 Oct 2019
Commented: Christine Tobler on 28 Oct 2019
Suppose I have two matrices A and B such that AB = BA, then how to compute the eigen vector common to both A and B? Both A and B are symmetric. Is the following command right:
[u,v] = eig(A,B)
does u give the common eigen vector to both A and B?

Daniel M on 7 Oct 2019
[v,D] = eig(A,B)
Yes, were you having issues with this? Do the values satisfy the general eigenvalue problem Av = DBv?
JYOTHI R on 7 Oct 2019
only the diagonal elements match
Christine Tobler on 28 Oct 2019
Can you give us the .mat file with the matrices you are entering? The EIG command with two inputs should give a result such that the following is small:
[U, D] = eig(A, B);
norm(A*U - B*U*D)
If this is not the case for your input matrices, this would likely mean that the pair (A, B) has some degenerate eigenvalues (the simplest example of those is when A = 0 and B = 0, so the eigenvalue would be 0/0).