The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems

Delve into the third lecture on extending complex numbers to handle spatial rotations and Hamilton's quaternion discovery. Explore a concise yet logically clear framework for this remarkable structure using 2x2 matrices with rational complex number entries. Learn how to prove quaternion arithmetic laws, incorporating linear algebra concepts like determinants and matrix traces. Examine an important visual model of quaternions and the key formula connecting them to three-dimensional rotations. Prepare for a content-rich lecture by approaching it in manageable segments and attempting the provided problems. This 56-minute video sets the stage for the final lecture, which will focus on practical applications of quaternions in rotations and their compositions, all without using transcendental concepts like angles, cosines, or sines.

Introduction
Introduction to quaternions
Laws of quaternions
Twobytwo matrices
Conjugation
Inverse Formula
Inner Product
Geometrical Representation
Understanding Rotations