I stumbled upon the 2d rotation matrix $$R(\theta)=\begin{pmatrix} \cos(\theta) & -\sin(\theta)\\ \sin(\theta) & \cos(\theta) \end{pmatrix}$$
which has determinant 1 because $$ \cos^2(\theta) + \sin^2(\theta) =1$$ So I thought what would happen if I replace the trig functions with hyperbolic ones, and when you do that you end up with determinant $$ \cosh^2(t) + \sinh^2(t) $$ but that tends to infinity so instead of having $$ -\sinh(t)$$ in the top right corner I replaced it with the positive version which gives us for determinant $$\cosh^2(t) - \sinh^2(t)$$ which is nicely equal to 1, but what's the name and purpose of this matrix?
from Hot Weekly Questions - Mathematics Stack Exchange
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