What are eigenvectors and eigennumbers?

1 Answer
Mar 2, 2017

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 AA is a linear transformation that we can define in a given subspace. We say that vec vv is an eigenvector of said linear transformation if and only if there exists a lambdaλ scalar such that:

A cdot vec v = lambda cdot vec vAv=λv

To this scalar lambdaλ we will call it eigenvalue associated with the eigenvector vec vv.