Eigenvectors in 2D

coefficients of matrix A:

a

11

a

12

a

21

a

22

Select the coefficients of the matrix

A

and drag the red arrow. The blue arrow shows the result of multiplication by

A

. An eigenvector is represented by the alignment of the two arrows; the eigenvalue is the ratio of their lengths. The arrows can align twice, once, or not at all, depending on whether A has two eigenvalues, a single one, or no real eigenvalues.