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stringy
#14
Apr21-11, 11:18 AM
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P: 90
Quote Quote by HallsofIvy View Post
No. Two matrices are similar if and only if they have the same eigenvalues and corresponding eigenvectors.
Would you mind clarifying this point? It's well known that a similarity transformation preserves the spectrum, but the eigenvectors?

The matrices

[ 0 1 ]
[ 0 0 ]

and

[ 0 0 ]
[ 1 0 ]

are similar via the permutation matrix

[ 0 1 ]
[ 1 0 ],

but they don't share the same eigenvectors.