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I understand that the special orthogonal group consists of matrices x such that [itex]x\cdot x=I[/itex] and [itex]detx=1[/itex] where I is the identity matrix and det x means the determinant of x. I get why the matrices following the rule [itex]x\cdot x=I[/itex] are matrices involved with rotations because they preserve the dot products of vectors. The part I don't get is why the matrices involved with rotation must have determinant 1.