What Does a Determinant of 1 in a Transformation Matrix Signify?

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Does it mean anything in particular about the transformation if the determinant of a transformation matrix is 1?
 
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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".
 
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.
 
Thanks, Dick. You are, of course, right.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

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