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    If there is a common eigenvector between two matrices A & B, how do I use it to find the eigenvector of the matrix AB??

    Many thx!!!
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    That doesn't make much sense. If v is an eigenvector of A and B, then it's going to also be an eigenvector of AB. Do you want to find the eigenvalue corresponding to this eigenvector for the matrix AB?
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    yes, thx
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    If A and B have a common eigenvector v, and if a and b are the respective eigenvalues, then:
    Av = av
    Bv = bv

    => ABv = A(Bv) = A(bv) = b(Av) = (ba)v = (ab)v
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    so the new eigenvalue of AB is ab?
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    yes
 
 
 
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Updated: April 11, 2006
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