Questions about Eigenspace

Question

I'm learning about Eigenspaces and have a few questions.

• Do eigenspaces, eigenvalues, and eigenvectors correspond to a tranformation or can a single vector space $V$ have an eigen-stuff?
• Is an eigenspace dependent on an eigenvalue or can multiple eigenvalues have the same eigenspace?

I thought I had a lot more questions. If I remember them I'll look it up before asking another question!

Thank you guys.

Answer 1

The eigendata refers to invariants of transformations. Different eigenvalues correspond to different eigenvectors/spaces, but not necessarily vice versa.