# What do zero eigenvalues mean?

What is the geometric meaning of a 3×3 matrix having all three eigenvalues as zero? I have interpretations in mind for 0, 1, and 2 eigenvalues being zero, but what about all of them?

For example, as mentioned in the comments, the matrices with all eigenvalues 0 are the nilpotent matrices, and these can have rank anywhere between $0$ and $n-1$