Duality, Polarity and Projective Linear Algebra - Differential Geometry Lecture 11

Explore the foundations of projective geometry in this lecture on differential geometry. Review the algebraic setup for projective points and lines using row and column 3-vectors. Discover how transformations work in projective geometry and delve into quadratic forms, symmetric bilinear forms, and associated projective 3x3 matrices. Examine the important example of Lorentz/Einstein/Minkowski geometry. Investigate concepts of perpendicularity and their relation to pole-polar duality between points and lines associated with the unit circle in the plane. Learn about the historical connections to Apollonius and the developments in Universal Hyperbolic Geometry. Gain insights into the mathematical foundations that underpin modern physics and geometry.