Home > Higher Algebra, Problem Solving > Traian Lalescu student contest 2011 Problem 1

## Traian Lalescu student contest 2011 Problem 1

Suppose $A \in \mathcal{M}(\Bbb{C})$. Prove that the sequence $(a_k)_{k \geq 0}$ is nondecreasing, where $a_k=rank(A^{k+1})-rank(A^k)$.

Traian Lalescu contest 2011 Problem 1