Theory - Eigenvector Viewer

Application

This applet helps you search for real eigenvectors and eigenvalues of 2x2 matrices.

An eigenvalue/vector is a solution of the equation

A x = k x where when multiplying a vector x with a matrix A, you want to know which vectors x will have a transformation Ax that is just a multiple of x. Typically you find for a given matrix, that when you have a solution to this, that there is a constant (or one of a few constant) multiples, or eigenvalues, that will be allowed. While there are many eigenvectors, you find that they are all simply multiples of each other, and there are only as many (and sometimes less) linearly independent eigenvectors and their associated eigenvalues as the dimension of the matrix (i.e. a 2x2 matrix will have no more than 2 eigenvalues and linearly independent eigenvectors).

Algorithm

For linear transformations, the matrix-vector product A x is given by

b1 = A11*x1 + A12*x2
b2 = A21*x1 + A22*x2

For more information see Mathworld's page on Eigenvalues.

Architecture

Java Applet