Thread: Multiple eigenvectors

Hi all,

I wonder if a matrix can have more than one eigenvectors (in a different direction) corresponding to one eigenvalue?

Thanks

Sure. Suppose you have an eigenvalue that has multiplicity two, and its corresponding eigenspace has dimension two. That means that you can take any linear combination of two differently oriented eigenvectors and still have an eigenvector. This is called the degenerate case.

Hint: What are the eigenvalues of the identity matrix and what are its eigenvectors?