TITLE: What is the minimum and maximum number of eigenvectors?
QUESTION [13 upvotes]: I am given the eigenvalues of a square, 8x8, matrix. They are all non-zero. I have determined that the matrix is diagonalizable and has an inverse. In one part of the problem, I am asked to find the maximum and minimum number of eigenvectors that the matrix could possibly have? 
Since A is diagonalizable does that mean it will have n linearly independent eigenvectors. So, is the max and min number of eigenvectors is 8?

REPLY [8 votes]: If $\vec v$ is an eigenvector, then so is $t \vec v$ for all real $t$. If they're asking about linearly independent eigenvectors, then you're right, but if they're just asking about eigenvectors, I would say the min and max is always infinite.