This template demonstrates the effect of multiplying a vector by a matrix. Enter a 2 × 2 matrix and press Start. The vectors and are displayed and drawn. The vector is the black vector in the lower graph, whereas the vector is the black vector in the upper graph. The upper graph shows the orbit made by the tip of as traverses the unit circle. The eigenpairs for the matrix are displayed on the left. If real, the normalized eigenvectors and their negatives are drawn in red and green in the lower graph. Moving the slider will change the angle the unit vector x makes with the positive -axis. As the slider is moved, the upper graph will display the vector and the varying norm of will be displayed on the left.