Determinant of matrix

1. Mar 11, 2008

ns5032

Does it mean anything in particular about the transformation if the determinant of a transformation matrix is 1?

2. Mar 12, 2008

HallsofIvy

Staff Emeritus
Yes, it does. That means the transformation does not change the length of a vector nor does it reverse the direction. It is, basically, a "rotation".

3. Mar 12, 2008

Dick

det=1 is not sufficient to show a transformation is a rotation, though the converse is true. Consider a matrix like [[1/2,0],[0,2]]. What is true is that the transformation doesn't change the volume of a region.

4. Mar 12, 2008

HallsofIvy

Staff Emeritus
Thanks, Dick. You are, of course, right.