Drag the circular handles on the two colored vectors in the vector space to the right to determine a basis for the vector space, and then drag the black point in either vector space to see it reflected in the other.
The left vector space is the space of coordinates for the vector space on the right, with respect to the given basis.
If the black point is to escape the square region on either side, its position is "clamped." This is to make sure you can always see the point in both vector spaces 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