Adventures in 9-space
The three by three matrix is a workhorse for mechanicians, yet the study of this tool is seldom addressed mathematically. One reason is that the space of such matrices is nine-dimensional, quite beyond diagrams and vision. The advantage of a mathematical investigation of the matrix space is clear in the study of two by two real matricies where rotations, shears, and squeezes correspond to area-preserving transformations of the plane. For transformations of space that preserve volume there is a much richer variety of phenomena that may correspond to mechanical events.
