Affine subspaces and transformations - 02 - affine subspaces
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 from machine learning. In this video, we describe the notion of affine span and affine subspaces. Briefly, these are almost geometrically the same as vector subspaces. The one difference is that they do not need to contain the zero vector.
Note: In the definition of affine subspace, the V in the expression "t\vec{u}+(1-t)\vec{v}\in V" should be replaced with A. The affine subspace here is called A.

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 transformations: https://youtu.be/PVhgAbh01ks

The previous video on Special Topics in Linear Algebra is on affine combinations: https://youtu.be/fWRm9dISpNk

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