Matrix Vector

Select entries of the matrix A using the sliders at right.

An "input vector" \(v\) is drawn in cyan in the graphing window, and the "output vector" \(Av\) is drawn in yellow. The coordinates of these two vectors are read out at upper right.

Control the input vector by dragging it in the graphing plane, by setting its rectangular coordinates using the sliders at left and below the graphing window, or by setting its polar coordinates using the \([r]\) and \([\theta]\) sliders at bottom.

Toggles at lower right enable display of the eigenvalue and, if the eigenvalues are real, the eigenlines. If the eigenline display is selected, a further toggle creates a visualization of the decomposition of both input and output vectors as linear combinations of eigenvectors. The summation parallelograms are displayed.