Linear algebra in hyperbolic space: Introduction to Gyrovector spaces

In this video we will talk about gyrovector spaces, the hyperbolic analogue of vector spaces. We will see how and why they were introduced, by focusing also on their relationship with thomas rotations and Einstein's velocity-addition formula. Timestamps: 00:00 Motivation behind vector spaces 04:53 Definition of a vector space 7:04 What is hyperbolic geometry? 10:18 Gyrovector spaces 10:54 Gyrogroups and relativistically admissible velocities 12:59 Thomas rotations and gyration 14:50 Mobius gyrogroups 15:50 Definitions of gyrogroups and gyrovector spaces Resources: http://johno.dk/mathematics/moebius.pdf https://www.semanticscholar.org/paper... https://www.semanticscholar.org/paper... Tags: #specialrelativity #thomasprecession #gyrogroups #gyrovectorspace #thomasrotations maths mathematics physics algebra gyrovector spaces geometry hyperbolic geometry special relativity Einstein velocity addition law Einstein velocity addition formula thomas precession thomas rotation Wigner rotation gyrogroups gyrovectors lobachevsky bolyai giuseppe peano H. Grassmann algebraic structures gyrocommutative gyrogroups gyrations mathematical formalism of special relativity linear algebra in hyperbolic spaces non euclidean geometries Euclid's fifth postulate Playfair's axiom vector spaces