1. Mar 11, 2008 #1

   ns5032

   

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

    

   ns5032, Mar 11, 2008
2. 
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3. Mar 12, 2008 #2

   HallsofIvy

   

   Science Advisor

   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".

    

   HallsofIvy, Mar 12, 2008
4. Mar 12, 2008 #3

   Dick

   

   Science Advisor

   Homework Helper

   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.

    

   Dick, Mar 12, 2008
5. Mar 12, 2008 #4

   HallsofIvy

   

   Science Advisor

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

    

   HallsofIvy, Mar 12, 2008

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