Circular points at infinity - Revision history

en>Rgdboer: /* References */ Sommerville

2014-06-12T20:55:26Z

References: Sommerville

← Older revision		Revision as of 22:55, 12 June 2014
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	~~Ed is what individuals contact me and my wife doesn~~'t like ~~it at all~~. ~~Mississippi~~ is ~~the only place~~ I've been ~~residing~~ in but I will have to move in a yr or two. ~~Office supervising is~~ my ~~occupation. To play domino~~ is ~~something~~ I ~~really appreciate doing~~.<br><br>~~Take a look at my homepage~~: ~~real psychics;~~ [http://~~koreanyelp~~.~~com~~/~~index~~.~~php?document_srl=1798&mid=SchoolNews koreanyelp~~.~~com~~],		I would like to introduce myself to you, I am Jayson Simcox but I don't like when individuals use my complete name. Office supervising is where my primary income arrives [http://cpacs.org/index.php?document_srl=90091&mid=board_zTGg26 free psychic] from but I've always wanted my personal company. For a while I've been in Alaska but I will have to move in a year or two. What me and my family members adore is bungee leaping but I've been using free psychic reading ([http://mybrandcp.com/xe/board_XmDx25/107997 http://mybrandcp.com/xe/board_XmDx25/107997]) on new issues lately.<br><br>My site: free psychic reading ([http://www.zavodpm.ru/blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going www.zavodpm.ru])

en>Magioladitis: fixed tag

2014-02-27T22:00:45Z

fixed tag

← Older revision		Revision as of 00:00, 28 February 2014
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	~~In [[mathematics]], a '''Euclidean distance matrix'''~~ is an '~~'n×n'' [[matrix (mathematics)\|matrix]] representing the spacing of a set of ''n'' [[point (geometry)\|points]] in [[Euclidean space]]~~. ~~If ''A''~~ is ~~a Euclidean distance matrix and the points <math>x_1,x_2,\ldots,x_n</math> are defined on ''m''-dimensional space, then the elements of ''A'' are given by~~		Ed is what individuals contact me and my wife doesn't like it at all. Mississippi is the only place I've been residing in but I will have to move in a yr or two. Office supervising is my occupation. To play domino is something I really appreciate doing.<br><br>Take a look at my homepage: real psychics; [http://koreanyelp.com/index.php?document_srl=1798&mid=SchoolNews koreanyelp.com],

	~~:<math>\begin{array}{rll}~~
	~~A & = & (a_{ij});~~
	\\
	~~a_{ij} & = & \|\|x_i - x_j\|\|_2^2~~
	~~\end{array}~~
	~~</math>~~

	~~where \|\|.\|\|<sub>2</sub> denotes~~ the ~~[[2-norm]] on '~~'~~'R'''<sup>m</sup>.~~

	~~==Properties==~~

	~~Simply put, the element ''a<sub>ij</sub>'' describes the square of the distance between the ''i''<sup> th</sup> and ''j''<sup> th</sup> points~~ in ~~the set. By the properties of the 2-norm (or indeed, Euclidean distance~~ in ~~general), the matrix ''A'' has the following properties.~~

	* All elements on the [[diagonal of a ~~matrix\|diagonal]] of ''A'' are zero (i~~.~~e. it~~ is ~~a [[hollow matrix]])~~.
	* The [[trace of a matrix\|trace]] of ''A'' is ~~zero (by the above property)~~.
	* ''A'' is [[symmetric matrix\|symmetric]] (i.e. ''a<~~sub~~>ij<~~/sub~~>~~'' = ''~~a~~<sub>ji</sub>'').~~
	* ''a<sub>ij</sub>''<sup>1/2</sup> <math>\le</math> ''a<sub>ik</sub>''<sup>1/2</sup> + ''a<sub>kj</sub>''<sup>1/2</sup> (by the [~~[triangle inequality]])~~
	* <math> a_{ij}\ge 0</~~math>~~
	* The number of unique (distinct) non-zero values within an ''N''-by-''N'' Euclidean distance matrix is bounded (above) by [''N''*(''N''-1)] / ~~2 due to the matrix being symmetric and hollow.~~
	* In dimension ''m'', a Euclidean distance matrix has [[Rank (linear algebra)\|rank]] less than or equal to ''m+2''. ~~If the points <math>x_1,x_2,\ldots,x_n<~~/~~math> are in [[General_position\| general position]], the rank is exactly ''m+2''~~.

	==~~See also==~~
	* [[Adjacency matrix]]
	* [[Distance matrix]]
	* [[Euclidean random matrix]]

	~~==References==~~
	* {{cite book \| author=James E. Gentle \| title=Matrix Algebra: Theory, ~~Computations, and Applications in Statistics \| publisher=[[Springer-Verlag]] \| date=2007 \| isbn=0-387-70872-3 \| page=299 }}~~

	~~[[Category:Matrices]]~~

	~~{{geometry-stub}}~~

en>David Eppstein: /* Coordinates */ ce

2014-01-28T20:26:58Z

Coordinates: ce

← Older revision		Revision as of 22:26, 28 January 2014
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	~~Hi there~~, ~~I am Alyson Pomerleau and I think it sounds fairly great when you say it. For many years she~~'~~s been working as~~ a ~~travel agent~~. ~~The favorite hobby for him and his kids~~ is ~~to perform lacross~~ and ~~he would never give it up~~. ~~North Carolina is~~ the ~~place he enjoys most but now he is contemplating other choices~~.<br><br>~~My webpage~~ ... ~~spirit messages~~ ([~~http:~~//~~Mybrandcp~~.~~com~~/xe/~~board_XmDx25~~/~~107997 just click~~ the ~~up coming~~ page])		In [[mathematics]], a '''Euclidean distance matrix''' is an ''n×n'' [[matrix (mathematics)\|matrix]] representing the spacing of a set of ''n'' [[point (geometry)\|points]] in [[Euclidean space]]. If ''A'' is a Euclidean distance matrix and the points <math>x_1,x_2,\ldots,x_n</math> are defined on ''m''-dimensional space, then the elements of ''A'' are given by

			:<math>\begin{array}{rll}
			A & = & (a_{ij});
			\\
			a_{ij} & = & \|\|x_i - x_j\|\|_2^2
			\end{array}
			</math>

			where \|\|.\|\|<sub>2</sub> denotes the [[2-norm]] on '''R'''<sup>m</sup>.

			==Properties==

			Simply put, the element ''a<sub>ij</sub>'' describes the square of the distance between the ''i''<sup> th</sup> and ''j''<sup> th</sup> points in the set. By the properties of the 2-norm (or indeed, Euclidean distance in general), the matrix ''A'' has the following properties.

			* All elements on the [[diagonal of a matrix\|diagonal]] of ''A'' are zero (i.e. it is a [[hollow matrix]]).
			* The [[trace of a matrix\|trace]] of ''A'' is zero (by the above property).
			* ''A'' is [[symmetric matrix\|symmetric]] (i.e. ''a<sub>ij</sub>'' = ''a<sub>ji</sub>'').
			* ''a<sub>ij</sub>''<sup>1/2</sup> <math>\le</math> ''a<sub>ik</sub>''<sup>1/2</sup> + ''a<sub>kj</sub>''<sup>1/2</sup> (by the [[triangle inequality]])
			* <math> a_{ij}\ge 0</math>
			* The number of unique (distinct) non-zero values within an ''N''-by-''N'' Euclidean distance matrix is bounded (above) by [''N''*(''N''-1)] / 2 due to the matrix being symmetric and hollow.
			* In dimension ''m'', a Euclidean distance matrix has [[Rank (linear algebra)\|rank]] less than or equal to ''m+2''. If the points <math>x_1,x_2,\ldots,x_n</math> are in [[General_position\| general position]], the rank is exactly ''m+2''.

			==See also==
			* [[Adjacency matrix]]
			* [[Distance matrix]]
			* [[Euclidean random matrix]]

			==References==
			* {{cite book \| author=James E. Gentle \| title=Matrix Algebra: Theory, Computations, and Applications in Statistics \| publisher=[[Springer-Verlag]] \| date=2007 \| isbn=0-387-70872-3 \| page=299 }}

			[[Category:Matrices]]

			{{geometry-stub}}

en>Tkuvho: /* References */

2012-02-12T15:26:52Z

References

New page

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