What are eigenvectors and eigennumbers?

1 Answer
Mar 2, 2017

Answer:

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#.