Suppose matrix $A$ has eigenvalue 1 with corresponding eigenvector $\mathbb{x}$. If $BA$ is to have eigenvalue of 1 with the same eigenvector, what would be the requirement or condition for it?
Multiplication of matrices and requirements of eigenvectors
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linear-algebra
matrices
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0Well, then *also* $\,B\,$ must have the eigenvalue 1 with exactly the same eigenvector $\,x\,$...About your second question: it is a little weird, but in the bottom line is: of course no, as this would contradict directly the definition of eigevector. – 2012-12-27
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0(For the sake of continuity, the second question was whether a single eigenvector could have multiple eigenvalues) – 2012-12-27