What does the symbol $\stackrel{!}{=}$ in the context of quaternions mean?

Question

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?

Answer 1

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.