Orthogonal subspace | Wikipedia audio article
Channel: Subhajit Sahu
Date: 2019-02-18

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
00:04:49 2.2 Euclidean vector spaces
00:06:11 2.3 Orthogonal functions
00:10:00 2.4 Examples
00:10:25 2.4.1 Orthogonal polynomials
00:12:49 2.4.2 Orthogonal states in quantum mechanics
00:13:11 3 Art
00:14:37 4 Computer science
00:16:18 5 Communications
00:17:26 6 Statistics, econometrics, and economics
00:19:56 7 Taxonomy
00:21:46 8 Combinatorics
00:23:26 9 Chemistry and biochemistry
00:23:48 10 System reliability
00:24:11 11 Neuroscience
00:26:08 12 Gaming
00:26:50 13 Other examples
00:27:12 14 See also
00:27:49 15 Notes
00:28:44 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.