Question

Question #7e09b

Answer 1

Please see Explanation.

Explanation:

Definition:
If for a `ntimesn` matrix `A` exists such a nonzero vector `v` satisfying $$Av=\lambda v,$$ where `lambda` is a scalar, we say that `v` is an eigenvactor of the matrix `A` and `lambda` is an eigenvalue of the matrix `A` associated with the eigenvector `v`.

As for where to find them in real life:
I'm not very sure but I think I saw something about something about applications of eigenvalues in quantum mecanics (but maybe it is 'too real life'). Also searching for aplications of The Perron-Frobenius Theorem may bring you closer to your answer.