Linear Transformation
Select one of the pre-defined linear transformation types and adjust the "amount" slider to define a linear transformation. The plot will then show you an input vector , which you can drag to change, and its corresponding output vector . Alternatively, select the "Custom" transformation and drag the vectors and to define the outputs for the two standard basis vectors and , respectively. Note: this means that the custom transformation is simply the matrix transformation corresponding to the 2x2 matrix whose columns are and , respectively.
If you check the "sum" or "multiple" boxes, you can verify that each linear transformation preserves vector addition and scalar multiplication, i.e. and . The vectors , , and can all be moved by dragging them.
If you check the "image" box, then you can see how the selected linear transformation affects an image. Each point in the original image corresponds to a vector (from the origin to that point), and transforming that vector reveals the location of the corresponding point in the transformed image.