Introduction to Linear Algebra - Wild Linear Algebra A 1 - NJ Wildberger

Explore the foundations of linear algebra in this comprehensive lecture, the first in a series that approaches the subject as "Linear Algebraic Geometry." Delve into the affine grid plane, vectors, and coordinate systems, learning essential vector operations and how to describe vectors using different coordinate systems. Tackle the fundamental problem of linear algebra: inverting linear coordinate changes. Discover general solutions in one and two dimensions, and engage with thought-provoking questions and exercises. Ideal for first-year college students, motivated high schoolers, teachers, and math enthusiasts seeking a more geometric and natural approach to this crucial mathematical field.

Intro
Course Overview
What is Linear Algebra
Two Dimensional Affine Grid Plane
Vectors and Coordinates
Refining the Grid Plane
Essential Vector Operations
Describing Vectors with Two Different Coordinate Systems
Generalizing Coordinate Transformations
Main problem of Linear Algebra
General Solution in One and Two Dimensions
Outstanding Questions
Exercises