# Does common eigenvectors between two matrices A,B implies some property for the vectors?

If there are two matrixes that they have common eigenvectors for some eigenvalues that implies that those two matrixes are identical? What can we say for those two matrices?

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Consider $\bigl(\begin{smallmatrix} 1 & 1 \\ 0 & 1 \end{smallmatrix}\bigr)$ and $\bigl(\begin{smallmatrix} 1 & 2 \\ 0 & 1 \end{smallmatrix}\bigr)$, all their eigenspaces are identical, but the matrices aren't identical. – nik Sep 25 '12 at 9:36
What can we say about the geometry of those matrices if we represent them in the euclidean space? – curious Sep 25 '12 at 9:46