Examples of vector spaces | Wikipedia audio article
Channel: wikipedia tts
Date: 27/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Examples_of_vector_spaces


00:00:21 1 Trivial or zero vector space
00:01:01 2 Field
00:01:41 3 Coordinate space
00:05:37 4 Infinite coordinate space
00:07:36 5 Product of vector spaces
00:07:55 6 Matrices
00:08:33 7 Polynomial vector spaces
00:08:46 7.1 One variable
00:08:56 7.2 Several variables
00:09:53 8 Function spaces
00:10:17 8.1 Generalized coordinate space
00:11:54 8.2 Linear maps
00:14:19 8.3 Continuous functions
00:15:09 8.4 Differential equations
00:15:35 9 Field extensions
00:16:00 10 Finite vector spaces
00:16:07 11 References
00:16:58 (dimFV)(dimKF)For example Cn, regarded as a vector space over the reals, has dimension 2n.
00:17:08 Finite vector spaces
00:17:18 Apart from the trivial case of a zero-dimensional space over any field, a vector space over a field F has a finite number of elements if and only if F is a finite field and the vector space has a finite dimension. Thus we have Fq, the unique finite field (up to isomorphism) with q elements. Here q must be a power of a prime (q



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SUMMARY
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This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis.
Notation. We will let F denote an arbitrary field such as the real numbers R or the complex numbers C. See also: table of mathematical symbols.