Sometimes a change of notation can advance thought. In today's blog the tradition of numerals 6,7,8, and 9 will be challenged.
Suppose the five letters a, b, c, d, and e are used to represent numbers satisfying
a + 1 = 0, b + 2 = 0, c + 3 = 0, d + 4 = 0, e + 5 = 0.
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.