Wednesday, 27 May 2015

linear algebra - An example of a square matrix with the same eigenvectors but different eigenvalues

Is there an example such that A and B, three by three, that have the same eigenvectors, but different eigenvalues?



What would be the eigenvectors and eigenvalues if it exists because I'm stuck on this practice problem.



I know that if matrices A and B can be written such that AB=BA, they share the same eigenvectors, but what about their eigenvalues? precisely if they're squared matrices (3×3 case)

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