Question

What are eigenvectors and eigennumbers?

Answer 1

An eigenvector is a vector that transforms by a linear operator in other vector in the same direction. Eigenvalue (eigennumber is not used) is the proportionality factor between the original eigenvector and the transformed one.

Explanation:

Suppose `A` is a linear transformation that we can define in a given subspace. We say that `vec v` is an eigenvector of said linear transformation if and only if there exists a `lambda` scalar such that:

`A cdot vec v = lambda cdot vec v`

To this scalar `lambda` we will call it eigenvalue associated with the eigenvector `vec v`.