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If I am given a matrix and told to find a basis for its eigenspace, does that just mean find the eigenvectors of the matrix? In my understanding, an eigenspace of an eigenvalue $\lambda$ is the set of degenerate eigenvectors associated with it, but what about the eigenspace of a matrix? Thanks.

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    Does this answer your question: http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors#Eigenspace.2011-11-06

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