I have a (3 x N) matrix of column rank 2. If each column is treated as a point in 3-space, then connecting the points draws out some planar shape. What operation can I apply such that this planar shape is transformed onto the x-y axis, so that the shape is exactly the same, but is now described fully by x-y coordinates in a (2 x N) matrix? I feel like there should be a (2 x 3) matrix that would do this, but I can't figure out what it should be. (I have a hunch that I'm looking for a mapping that is isometric and conformal... some kind of rotation?). Also, I'd like to be able to generalise to higher dimensions.