Linear Algebra - Least Squares Approximation - 02 - Fundamental Theorem
Channel: Arthur Parzygnat
Date: 08/01/2019

A least squares approximation attains a simple form when the subspace is the column space of some matrix. This renders computing least squares approximations a more tractable problem. A proof of this theorem is provided in this video. Subsequent videos use the result (the proof is never used). The very ending of this proof became a little convoluted (my bad).

This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.

The next video on Special Topics in Linear Algebra is on Fitting data to a straight curve Part 1: https://youtu.be/mpkPJfCDWTU

The previous video on Special Topics in Linear Algebra is an introduction to the least squares problem: https://youtu.be/f0dyfIx5K-Q

These videos were created during the 2019 Spring semester at the UConn CETL Lightboard Room.