I was wondering if I could have help with the following problem:
Let A be an n by n matrix and let lambda be an eigenvalue of A whose eigenspace has dimension k, where 1<k<n. Show that lambda is an eigenvalue of A with multiplicity at least k.
I'm supposed to use the following theorem:
If B is similar to A, then A and B have the same eigenvalues (the solutions to both of their characteristic equations are the same).
Relevant fact: I know that because A is n by n that A has n linearly independent column vectors. Does this have anything to do with A having k linearly dependent eigenvectors?