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