I hope this website will become a valuable resource for everyone learning and doing linear algebra. Here are key links:

Introduction to Linear Algebra, 5th Edition (2016 edition) Introduction to Linear Algebra, 6th Edition (2023 edition) Accessibility

Our recent textbook Linear Algebra for Everyone starts with the idea of independent columns This leads to a factorization A = CR where C contains those independent columns from A

Textbooks, Websites, and Video Lectures Part 1 : Basic Ideas of Linear Algebra 1.1 Linear Combinations of Vectors 1.2 Dot Products v · w and Lengths || v || and Angles θ 1.3 Matrices …

Our recent textbook Linear Algebra for Everyone starts with the idea of independent columns This leads to a factorization A = CR where C contains those independent columns from A

I am happy for you to see this Fifth Edition of Introduction to Linear Algebra. This is the text for my video lectures on MIT’s OpenCourseWare (ocw.mit.edu and also YouTube).

Linear combinations can fill all of space, or only a plane. We need a picture to show the crucial difference between u, v, w (the first example) and u, v, w∗ (all in the same plane).

You need to know about the video lectures for MIT’s Linear Algebra course Math 18.06. Those videos go with this book, and they are part of MIT’s OpenCourseWare.

Gilbert Strang, Introduction to Linear Algebra, 6th Edition (2023) 1. When can lines of lengths r,s,t form a triangle? They must satisfy the strict triangle inequalities r < s+t s < r +t t < r +s If we allow equality, …

4 v + w = (2, 3) and v − w = (6, −1) will be the diagonals of the parallelogram with