which also have negative determinant and form a valid parity transformation. Then, combining them with rotations (or successively performing x -, y -, and z -reflections) one can recover the particular parity transformation defined earlier. The first parity transformation given does not work in an even number of dimensions, though, because it results in a positive determinant. In even dimensions only the latter example of a parity transformation (or any reflection of an odd number of coordinates) can be used.