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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.

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+1 for "wash my socks" :-) – Gottfried Helms Apr 20 '11 at 12:07
currently investigating python-scitools module – d3vid Apr 28 '11 at 5:59

I do not know any application which can do this for you. But visualisation of matrices is not a difficult task. You can make it yourself using NumPy and MatPlotLib libraries for this (speaking about Python).

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