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.

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- CC-BY-SA-4.0
- Created On
- January 3rd, 2017
- 4 years ago
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- 3
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- Video
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- English
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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.

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- CC-BY-SA-4.0
- Created On
- June 9th, 2017
- 3 years ago
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- 3
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- Video
- Timeframe
- Pre-class
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- Language
- English
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- 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
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- 2
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- Video
- Language
- English
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- 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
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- 2
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- Language
- English
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- text/html