A quadratic 10x10 point array of edge length 1 is grouped in the z plane . One edge point is colored in red and connected to the origin by a red vector. One can shift the array by drawing the red point with the mouse to any position in the plane.
The size of the array can be decreased by a slider until just the red point is visible. This allows you to experiment with a single point. The scale of the coordinate system is adjusted to the size of the array.
A second point (green factor vector) is multiplied with every point of the array. By drawing the blue arrowhead with the mouse, the absolute size and direction of the green factor vector can be changed.
In the u plane the result of the multiplication is displayed. The angle of the product vector is the sum of the angles of the vectors. The length of the product vector is the product of the lengths of the vectors. The array is rotated by the positive angle of the factor vector. Accordingly its orientation is changed by the angle of the factor vector.
The reset button resets to the default position.