I have encountered a bit a of problem when visualizing linear maps, a colleague of mine seems to have no problem and can tell purely by the matrix in question what the transformed space will look like even in $3D$.
I just cant seem to do it even when using a visualization tool often the image in my head seems to be wrong in some respects.
I have taken vector calculus and never had a problem visualizing things in $3D$ any suggestions of how i can rectify this problem?