Basis change toy

The vector space on the right has two separate bases: one given by a green and a red vector, and the other by blue and yellow. Drag the circular handles on the vectors in this space to choose the two basis matrices displayed in the center.

The change of basis matrix for the chosen bases is displayed on the left. This transforms coordinates relative to the first basis into coordinates relative to the second.

Drag the black point in any of the three vector spaces to see its corresponding position in the other two. If the black point is to escape the square region in any of the vector spaces, its position is "clamped." This is to make sure you can always see the point in each vector space at all times.

If the vectors are linearly dependent (that is, if the basis matrix has a zero determinant), then dragging the black point is temporarily disabled.

©2016 Kyle Miller