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Determinant of matrix

  • Thread starter ns5032
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Does it mean anything in particular about the transformation if the determinant of a transformation matrix is 1?
 

Answers and Replies

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

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