Orthogonal subspaces | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-17

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Orthogonality


00:00:52 1 Etymology
00:01:33 2 Mathematics and physics
00:01:44 2.1 Definitions
00:04:48 2.2 Euclidean vector spaces
00:06:08 2.3 Orthogonal functions
00:09:54 2.4 Examples
00:10:20 2.4.1 Orthogonal polynomials
00:12:41 2.4.2 Orthogonal states in quantum mechanics
00:13:03 3 Art
00:14:29 4 Computer science
00:16:09 5 Communications
00:17:17 6 Statistics, econometrics, and economics
00:19:44 7 Taxonomy
00:21:34 8 Combinatorics
00:23:12 9 Chemistry and biochemistry
00:23:34 10 System reliability
00:23:57 11 Neuroscience
00:25:53 12 Gaming
00:26:35 13 Other examples
00:26:56 14 See also
00:27:33 15 Notes
00:28:27 16 References



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SUMMARY
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In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.  Two elements u and v of a vector space with bilinear form B are orthogonal when B(u, v) = 0.  Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis.
By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry.