Visualizing Matrix Bases and Transforms

There are transformations that can be produced using matrices with just the three integers . Some 33 of these are degenerate, in that the transformed matrix loses a dimension and has a zero determinant. This Demonstration considers all of these cases, initially with the unit matrix as the base to be transformed. Deselect the checkbox to use an arbitrary base matrix of a different size. Transform number 69 is the identity matrix and number 53 is its transpose, the antidiagonal matrix.