Linear Algebra 5.4 Mathematical Models and Least Squares Analysis

Most of this video focuses on the understanding of the components of least squares analysis. If you need to understand the “how” rather than “why”, skip to the last 10-15 minutes.

Video Chapters:
0:00 Introduction
0:08 Orthogonal Subspaces
1:49 Orthogonal Complement
2:44 Orthogonal Complement Example
5:27 Direct Sum
6:44 Properties of Orthogonal Subspaces
7:45 Projection onto a Subspace
10:37 Projection onto a Subspace Example
14:31 Visualizing the Projectio onto a Subspace
16:10 The Fundamental Subspaces of a Matrix
18:03 Find the Fundamental Subspaces of a Matrix
20:15 Why are Fundamental Subspaces Important?
21:17 What is a Least Squares Solution?
24:06 How to Find x
26:10 Practice – Calculate ATA and ATB
28:38 Practice – Solve for x
29:58 Visualize the Solution
30:25 Practice – Find the Orthogonal Projection
31:20 Visualize the Solution
33:06 Practice – Find the Error
34:28 Mathematical Model – Find Least Squares Polynomial
38:52 Mathematical Model Practice
40:45 Up Next
Textbook: Elementary Linear Algebra 8e, Ron Larson

Slide Decks: https://bellevueuniversity-my.sharepoint.com/:f:/g/personal/kbrehm_bellevue_edu/IgDVnTt2BohsRLsMfseN5FijAXYDd49YlIkHeq5cfmCxG2g?e=ZwTt3c

Playlist: https://youtube.com/playlist?list=PLl-gb0E4MII1RjTV2GegmXFTJwTrek8OI&si=g3Xc3yHB5GkmxMF4