A program to visualize Linear Algebra? I am asking here because I believe you have some idea of a good visualizer 3d program to see what are really: eigenvectors, subspaces, rowspaces, columnspaces and just answers on normal matrix multiplication visualized. 
It's easy to calculate, but it's hard to visualize I think. 

It depends how you want to go about it. With this I mean that you need to structure the way you want to visualize things for example eigen vectors a good way to visualize them is by doing 3D or 2D orthogonal transformations a very cool application with great visual implications is Principal components analysis for example.
If you are familiar with programing I would recommend matplotlib its python and its very easy syntax and like I said you can visualize things such as linear transformations on 3D objects in very nice ways.
Additionally wolfram alpha gives you little matrix heatdiagrams and graphs for adjecency matrices if you are after something like.
