# Eigenvectors by Hand

Eigenvectors by Hand

A linear map transforms vectors into other vectors. A nonzero vector (boldface in this Demonstration) is an eigenvector when its image (dotted here) is a multiple of itself; this occurs when the colored parallelogram vanishes. Drag the vectors until they become eigenvectors. If you manage to hit a basis of eigenvectors, then in this new basis the matrix of the linear map (shown above the graphic) becomes diagonal.