Ufyukyu

0 $begingroup$ I'm representing hyperbolic vectors using the Minowski hyperboloid: $x_0^2 - x_1^2 - x_2^2 = 1$ . I understand that the distance between two hyperbolic vectors of this form is $acosh(B(u, v))$ where $B(u, v) = u_0v_0 - u_1v_1 - u_2v_2$ . But I cannot for the life of me figure out a simple way to perform scalar and vector multiplication with the expected results using these vectors. For scalar multiplication, for example, I have tried the following: For one dimensional hyperbolic vectors ( $1=x_0^2-x_1^2$ ), I have understood that scalar multiplication is equivalent to multiplying the hyperbolic angle. If $v = [cosh theta, sinhtheta]$ , then $2v$ should be $[cosh2theta, sinh2theta]$ . Finding $theta$ should be as trivial as taking $acos(x_0$ ). Things get complicated in 2d hyperbolic ...