Dot Products, Pythagoras' Theorem, and Generalizations - Wild Linear Algebra A - NJ Wildberger
Offered By: Insights into Mathematics via YouTube
Course Description
Overview
Explore the foundations of metrical geometry through a novel, algebraic approach to linear algebra in this 28-minute video lecture. Learn about dot products, their bilinear and symmetric properties, and how they relate to Pythagoras' theorem. Discover how to define perpendicularity and quadrance of vectors using purely algebraic concepts, allowing for work with rational numbers. Follow along as an algebraic proof of Pythagoras' theorem is presented, demonstrating its fundamental importance in linear algebra. Conclude by examining symmetric bilinear forms and their connection to 2x2 matrices, setting the stage for understanding relativistic geometry introduced by Einstein and Minkowski.
Syllabus
Introduction
The fundamental dot product of vectors
Symmetric property of the dot product
Pythagoras Theorem via Linear Algebra
Transpose
Taught by
Insights into Mathematics
Related Courses
Maths - Basic angles, distances and coordinatesUdemy Triangles - CBSE Class 10 Mathematics
YouTube GCSE Maths Revision - Geometry and Measures
YouTube O Level Trigonometry
zainematics via YouTube Trigonometry O Level
zainematics via YouTube