Definition of subspace, arbitrary vector space

math.la.d.vsp.subspace.arb


Preliminaries: 1. What is a subset? 2. How to verify a set is a subset of another set? 3. Notations and language of set theory related to subsets. In this video, we introduce the definition of a subspace. We go through a preliminary example to figure out what do subspaces of R^2 look like, and we will continue to talk about how to verify a subset of a vector space is a subspace in later videos.

License
CC-BY-SA-4.0
Created On
January 3rd, 2017
3 years ago
Views
3
Type
 Video
Perspective
 Introduction
Language
 English
Content Type
text/html; charset=utf-8

In this video, I'll explain why we only need to test 2 axioms (among the 10 axioms in the definition of a vector space) when figuring out if a subset is a subspace.

License
CC-BY-SA-4.0
Created On
June 9th, 2017
3 years ago
Views
3
Type
 Video
Timeframe
 Pre-class
Perspective
 Introduction
Language
 English
Content Type
text/html; charset=utf-8

Definition of a subspace of a vector space; examples; span of vectors is a subspace.

Created On
September 3rd, 2017
3 years ago
Views
2
Type
 Video
Language
 English
Content Type
text/html; charset=utf-8

A subspace is a vector space that is contained within another vector space. So every subspace is a vector space in its own right, but it is also defined relative to some other (larger) vector space. We will discover shortly that we are already familiar with a wide variety of subspaces from previous sections.

License
GFDL-1.2
Submitted At
September 11th, 2017
 3 years ago
Views
2
Type
 Textbook
Language
 English
Content Type
text/html