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Simultaneous diagonalization of two matrices

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JYOTHI R
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?

  3 Comments

Daniel M
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?
Christine Tobler
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).

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