Let $A$ be an $n\times n$ complex matrix, and $C(A)$ be the vector space of all matrices that commute with $A$. I have to determinate if the dimension of $C(A)$ is greater or equal than $n$, or not.
If anyone can give me a hint, i think the answer is yes, but i am not sure what i have to use to prove it.
Best Answer
Hint: consider the Jordan canonical form of $A$. What can you say about matrices that commute with a Jordan block?