Linear Transformations for Eigenvectors/eigenvalues

This applet shows the effect of a linear transformation

. The effects of

on the blue vector

and the blue triangle are depicted as the red vector

and the red triangle. The matrix corresponding to

is called

. Recall that the column vectors of

are given by

and

, where

and

. Manipulate

and

to define a new linear transformation and see its corresponding matrix. You may also manipluate

and the blue triangle.

How to detect Eigenvector and Eigenvalue graphically by hand

Exercises For the following four exercises, find the matrix for the linear transformation corresponding to [list=5]

scaling by the factor 1/2.

reflection across the line

180 degree rotation about the origin.

projection onto the

-axis. [/list] For the next four exercises, describe the linear transformation given by the matrix [list=5]

[/list]