## Wednesday, March 14, 2012

### Eigenvalues and eigenvectors

This applet is based in the one on Linear mappings, being essentially the same with the option of displaying eigenvectors and eigenvalues.

The black vector represents the input of the linear application, it can be edited by click and drag. The red vector represents the result of the mapping. The mapping matrix can also be edited. Remember that not all linear mappings have real eigenvalues.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Questions:

· What happens if the black vector lies over an eigendirection? Is there any relation with the eigenvalues?

· Introduce the following matrix a = 0, b = 1, c = -1, d = 0. Move the vector and try to guess what the transformation represents. It has no real eigenvectors, why?

· Is it possible for a two dimensional linear mapping to have more than two eigenvectors? Why?

· What happens if we transform the application to a basis of eigenvectors?