Singular Values

In the diagram below, you may choose a matrix $A=\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ using the four sliders. You may also move the red vector ${\mathbf v}$ around the unit circle on the left and observe the vector $A{\mathbf v}$ and its length $|A{\mathbf v}|$ on the right.