Affine subspaces and transformations - 01 - affine combinations
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, for example, support vector machines from machine learning. In this video, we describe affine combinations algebraically and geometrically.

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 affine subspaces: https://youtu.be/ErCl7PCkoyc

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