Three-Dimensional Rotation Matrices
Taking the determinant of the equation RRT = Iand using the fact that det(RT) = det R, it follows that (det R)2 = 1, which implies that either detR = 1 or detR = −1. A real orthogonal n ×n matrix with detR = 1 is called a special orthogonal matrix and provides a matrix representation of a n-dimensional proper rotation1 (i.e. no mirrors ...
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