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.
For the next four exercises, describe the linear transformation given by the matrix