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Homework Help: Determinant of matrix

  1. Mar 11, 2008 #1
    Does it mean anything in particular about the transformation if the determinant of a transformation matrix is 1?
     
  2. jcsd
  3. Mar 12, 2008 #2

    HallsofIvy

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    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".
     
  4. Mar 12, 2008 #3

    Dick

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    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.
     
  5. Mar 12, 2008 #4

    HallsofIvy

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