Introduction to Universal Hyperbolic Geometry
What really made UHG click for me was this lecture:
This lecture basically explains this paper visually.
Starting out with two dimensions
\(\mathbb{F}^2 \quad v=(x, y) \quad A=\left(\begin{array}{ll}a & b \\ b & c\end{array}\right)\) fixed then define
\[\begin{aligned} & v_1 \cdot v_2=v_1 A v_2^{\top}=\left(x_1 y_1\right)\left(\begin{array}{ll} a & b \\ b & c \end{array}\right)\binom{x_2}{y_2} \\ & =a x_1 x_2+b x_1 y_2+b x_2 y_1+c y_1 y_2 \end{aligned}\]Generalizing to 3D
