A linear transformation of period two. Since a linear transformation has the form,
(1)
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applying the transformation a second time gives
(2)
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For an involutory, , so
(3)
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Since each coefficient must vanish separately,
(4)
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(5)
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(6)
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Equation (5) requires . Taking in turn requires that , giving , i.e., the identity map, while taking gives , so
(7)
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which is the general form of a line involution.