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## Homework Statement

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.

## Homework Equations

## 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.