Area and Volume - Wild Linear Algebra A | NJ Wildberger
Explore the fundamental concepts of area and volume in linear algebra through this comprehensive lecture. Delve into the pictorial treatment of area before transitioning to an algebraic formulation using bi-vectors, introduced by Grassmann in the 1840s. Discover the central role these concepts play in underpinning the entire subject and their connection to the rich theory of determinants. Learn about the general formula for the area of a parallelogram, considered one of the most important formulas in mathematics. Investigate bi-vectors and their applications in physics, including torque, linear momentum, and electromagnetism. Examine the properties and operations of bi-vectors in the plane, including distributive laws and their relationship to base vectors. Extend the concepts to three-dimensional space, exploring tri-vectors and their use in computing volume. Gain practical experience through exercises that reinforce the learned material, providing a solid foundation for further study in linear algebra and related fields. Read more