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I was reading "Physics from Symmetry" by Jakob Schwichtenberg recently. And in part 3 of chapter 3, he goes over quaternions and I found the following statement:
The set of unit quaternions $q = a\textbf{1} + b\textbf{i} + c\textbf{j} +d\textbf{k}$ satisfy the condition $$q^{\dagger}q \stackrel{!}{=} 1$$ Where, $q^\dagger = (q^{*})^T$
What does the symbol $\stackrel{!}{=}$ mean?

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    $\begingroup$ That's not common notation but it seems the author is making a distinction between an implied equality and one that defines a property. The characterization of unit quaternions you describe holds just as well if you replaced that with an ordinary equal sign. $\endgroup$
    – j0equ1nn
    Commented Mar 27, 2020 at 7:39
  • $\begingroup$ Oh okay, thanks @j0equ1nn! $\endgroup$
    – Pugs
    Commented Mar 27, 2020 at 7:55

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It means “should be equal”, i.e. this is a condition being imposed, rather than an equation that holds generally. It’s not specific to the context of quaternions.

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  • $\begingroup$ All right, thank @joriki! $\endgroup$
    – Pugs
    Commented Mar 27, 2020 at 7:56

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