I'm looking for a FLOSS application (Windows or Ubuntu but preferably both) that can help me visualize matrix transformations in 2- and 3-space.
So I'd like to be able to enter a vector or matrix, see it in 2-space or 3-space, enter a transformation vector or matrix, and see the result. For example, enter a 3x3 matrix, see the parallelepiped it represents, enter a rotation matrix, see the rotated parallelepiped.
Bonus points for ability to calculate area/volume, animate, change colours, visualize higher dimensions, wash my socks.