# How to prove that if A is a diagonalizable matrix, then the rank of A

How to prove that if A is a diagonalizable matrix, then the rank of A is the number of nonzero eigenvalues of A.
Thanks and regard.

Landau
If $$A$$ is similar to $$B$$ then $$\textrm{rk}(A)=\textrm{rk}(B)$$, then consider the rational canonical form, and it follows as Landau stated above.