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Is there a common way to express the idea of "$\pm 1$" using words, ideally without spelling out "plus or minus one". Not that the absolute value is one, but that the value is either 1 or -1.

For example, without using the symbols "$\pm 1$", how would one say "If $Q \in M_{n \times n}(\mathbb{R})$ is orthogonal, then $\det(Q) = \pm 1$"?

The Big Lebesgue
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What about $|\det(Q)| = 1$? Isn't it equivalent to $\det(Q) = \pm 1$ ? Or would you prefer "$\det(Q)$ of square $1$"?

J.-E. Pin
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  • I like the "of square one" idea since it works in the reals, but this allows for multiple possibilities in complex values. It's a little like saying "of norm one". – The Big Lebesgue Jan 26 '18 at 06:29
  • Right. But for integer matrices, there is a proper name as you wish: unimodular. Unfortunately, I don't think it is used for complex matrices. – J.-E. Pin Jan 26 '18 at 06:44
  • This could be what I'm looking for. Do you know the etymology of unimodular ? I found this link to it on Wiktionary defining it as "of a lattice or matrix having a determinant of 1 or -1". Would you call it an abuse of terminology to talk about either orthogonal matrices or their determinant having the unimodular property? – The Big Lebesgue Jan 28 '18 at 01:29