Transformation toy: eigenvector edition
Drag the circular handles on the two colored vectors in the
vector space to the right to choose the columns of a matrix
of a linear transformation.
The locations of the points of the cat image are
transformed according to the transformation, and the
resulting image is given on the right.
The eigenvectors of the matrix, when there are real
eigenvectors, are drawn spanning a grid in both the left and
right vector spaces. Since matrices scale eigenvectors, the
grid on the right is the grid on the left but scaled by
different amounts in each eigenvector direction. Thus, the
parallelograms are going "in the same direction" as the ones
on the left.
Compare corresponding parallelogram regions and see how
they are stretched.
©2016 Kyle Miller