1. The problem statement, all variables and given/known data Let V be a finite dimensional vector space over ℂ . Show that any linear transformation T:V→V has at least one eigenvalue λ and an associated eigenvector v. 2. Relevant equations 3. The attempt at a solution Hey everyone I've been doing sample questions in the build up to an exam and I came across this. Any help would be greatly appreciated as I'm struggling a bit. Here is what I know: λ is an eigenvalue if there exists a non-zero vector v∈V such that Tv = λv. I also read this for complex: q(λ) = det (λI - T), where the zeros of q(λ) in ℂ are the eigenvalues of T. What does the second point mean or how would I answer this properly. Thanks in advance.