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# FP3 Eigenvalue watch

1. 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!!!
2. 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?
3. yes, thx
4. 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
5. so the new eigenvalue of AB is ab?
6. yes

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Updated: April 11, 2006
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