Eigenvectors in 2D
Select the coefficients of the matrix and drag the red arrow. The blue arrow shows the result of multiplication by . 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.
This was inspired by an example in the ATLAST (Augmenting the Teaching of Linear Algebra through the use of Software Tools) project.
"Eigenvectors in 2D"
Wolfram Demonstrations Project
Published: September 28 2007