Affine subspaces and transformations - 03 - affine transformations
Channel: Arthur Parzygnat
Date: 2019-12-24

Affine transformations generalize both linear transformations and equations of the form y=mx+b. They are ubiquitous in support vector machines and neural networks from machine learning. In this video, we finally define affine transformations. They are functions that take affine combinations to affine combinations. All affine transformations between Euclidean spaces are of the form y=Mx+b. 

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 composition of affine transformations: https://youtu.be/vQDG2QG0qw8

The previous video on Special Topics in Linear Algebra is on affine subspaces: https://youtu.be/ErCl7PCkoyc

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