Instructions - Eigenvector Viewer

Purpose

The purpose of the Eigenvector Viewer is to allow you to see linear transformations in 2 dimensions by entering a matrix and clicking on the screen to input a vector x, and see a resultant vector b = A x.

By finding the input vectors that overlap with the output vectors, one can find the real eigenvectors and eigenvalues of the matrix.

Fundamentals

Enter your matrix in the space provided, and modify the graph scale as needed.

Features

The "sweep" button will let you put the applet on auto-pilot, sweeping out a full 360 degrees to search for eigenvectors and eigenvalues.

Things to try

What are the real eigenvectors of:

1 2
3 4

1 1
-1 2

1 0 
0 1

1 2
2 4