Logarithm of a matrix - Revision history

en>TakuyaMurata: /* A Lie group theory perspective */

2014-12-06T01:34:28Z

A Lie group theory perspective

← Older revision		Revision as of 03:34, 6 December 2014
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	The ~~name of the author is Figures but it's not the most masucline name out there. South Dakota~~ is ~~her beginning location but she needs to transfer simply because of her family~~. ~~Body developing~~ is what ~~my family~~ and ~~I enjoy. Hiring~~ has been ~~my profession for some time but~~ I'~~ve currently utilized for another 1~~.<br><br>~~Feel free to visit~~ my ~~weblog :~~: [http://~~www~~.~~youporn-nederlandse~~.~~com~~/~~blog~~/~~117384~~ over the counter std test]		The writer is called Irwin. Managing individuals is what I do and the salary has been truly fulfilling. California is our birth place. To do aerobics is a thing that I'm completely addicted to.<br><br>my web site: [http://Mtomtech.Co.kr/bbs/?document_srl=92816 over the counter std test]

en>Airwoz: /* Properties */

2014-02-25T21:08:31Z

Properties

← Older revision		Revision as of 23:08, 25 February 2014
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	~~{{for\|the Klein '''quartic'''\|Klein quartic}}~~		The name of the author is Figures but it's not the most masucline name out there. South Dakota is her beginning location but she needs to transfer simply because of her family. Body developing is what my family and I enjoy. Hiring has been my profession for some time but I've currently utilized for another 1.<br><br>Feel free to visit my weblog :: [http://www.youporn-nederlandse.com/blog/117384 over the counter std test]

	~~In [[mathematics]], the lines of a 3-dimensional [[projective space]], ''S'', can be viewed as points~~ of ~~a 5-dimensional projective space, ''T''. In that 5-space,~~ the ~~points that represent each line in~~ '~~'S'' lie on a [[hyperbolic quadric]], ''Q'' known as~~ the ~~'''Klein quadric'''~~.

	~~If the underlying [[vector space]]~~ of ~~''S''~~ is ~~the 4-dimensional vector space ''V'', then ''T''~~ has ~~as the underlying vector space the 6-dimensional [[exterior square]] Λ<sup>2</sup>~~'~~'V'' of ''V''. The [[line coordinates]] obtained this way are known as [[Plücker coordinates]]~~.

	~~These Plücker coordinates satisfy the quadratic relation~~
	: <~~math~~>~~p_{12} p_{34}+p_{13}p_{42}+p_{14} p_{23} = 0~~ <~~/math~~>
	~~defining ''Q'', where~~
	: ~~<math>p_{ij} = u_i v_j - u_j v_i</math>~~
	~~are the coordinates of the line [~~[~~Linear span\|spanned]] by the two vectors ''u'' and ''v''.~~

	~~The 3-space, ''S'', can be reconstructed again from the quadric, ''Q''~~: the planes contained in ''Q'' fall into two [[equivalence classes]], where planes in the same class meet in a point, and planes in different classes meet in a line or in the empty set. Let these classes be <math>C</~~math> and <math>C'<~~/~~math>~~. ~~The [[geometry]] of ''S'' is retrieved as follows:~~

	~~# The points of ''S'' are the planes in ''C''.~~
	~~# The lines of ''S'' are the points of ''Q''.~~
	~~# The planes of ''S'' are the planes in ''C''’~~.

	~~The fact that the geometries of ''S'' and ''Q'' are isomorphic can be explained by the [[isomorphism]] of the [[Dynkin diagram]]s ''A''<sub>3<~~/~~sub> and ''D''<sub>3<~~/~~sub>.~~

	~~==References==~~

	* {{citation\|title=Twistor Geometry and Field Theory\|first1=Richard Samuel\|last1= Ward\|first2= Raymond O'Neil, Jr.\|last2= Wells\|author2-link=Raymond O. Wells, Jr.\|publisher=Cambridge University Press\|year= 1991\|isbn=978-0-521-42268-0}}.

	~~{{geometry-stub}}~~
	~~[[Category:Projective geometry]]~~
	~~[[Category:Quadrics]~~]

en>Mgnbar: /* Existence */ "complex" was used to mean "non-real complex"

2014-01-26T22:07:39Z

Existence: "complex" was used to mean "non-real complex"

← Older revision		Revision as of 00:07, 27 January 2014
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	~~Greetings! I am Myrtle Shroyer~~. ~~Her husband and her reside~~ in ~~Puerto Rico but she will have to move one working day or an additional~~. ~~I utilized to be unemployed but now I am a librarian and~~ the ~~salary~~ has ~~been really fulfilling~~. ~~To gather badges is what her family members and her appreciate~~.<br><br>~~Feel free to visit my weblog~~ :: [~~http:~~//~~www~~.~~dhspoteh~~.co.kr/xe/~~index~~.~~php?document_srl~~=~~331302&mid~~=~~Sports std home test~~]		{{for\|the Klein '''quartic'''\|Klein quartic}}

			In [[mathematics]], the lines of a 3-dimensional [[projective space]], ''S'', can be viewed as points of a 5-dimensional projective space, ''T''. In that 5-space, the points that represent each line in ''S'' lie on a [[hyperbolic quadric]], ''Q'' known as the '''Klein quadric'''.

			If the underlying [[vector space]] of ''S'' is the 4-dimensional vector space ''V'', then ''T'' has as the underlying vector space the 6-dimensional [[exterior square]] Λ<sup>2</sup>''V'' of ''V''. The [[line coordinates]] obtained this way are known as [[Plücker coordinates]].

			These Plücker coordinates satisfy the quadratic relation
			: <math>p_{12} p_{34}+p_{13}p_{42}+p_{14} p_{23} = 0 </math>
			defining ''Q'', where
			: <math>p_{ij} = u_i v_j - u_j v_i</math>
			are the coordinates of the line [[Linear span\|spanned]] by the two vectors ''u'' and ''v''.

			The 3-space, ''S'', can be reconstructed again from the quadric, ''Q'': the planes contained in ''Q'' fall into two [[equivalence classes]], where planes in the same class meet in a point, and planes in different classes meet in a line or in the empty set. Let these classes be <math>C</math> and <math>C'</math>. The [[geometry]] of ''S'' is retrieved as follows:

			# The points of ''S'' are the planes in ''C''.
			# The lines of ''S'' are the points of ''Q''.
			# The planes of ''S'' are the planes in ''C''’.

			The fact that the geometries of ''S'' and ''Q'' are isomorphic can be explained by the [[isomorphism]] of the [[Dynkin diagram]]s ''A''<sub>3</sub> and ''D''<sub>3</sub>.

			==References==

			* {{citation\|title=Twistor Geometry and Field Theory\|first1=Richard Samuel\|last1= Ward\|first2= Raymond O'Neil, Jr.\|last2= Wells\|author2-link=Raymond O. Wells, Jr.\|publisher=Cambridge University Press\|year= 1991\|isbn=978-0-521-42268-0}}.

			{{geometry-stub}}
			[[Category:Projective geometry]]
			[[Category:Quadrics]]

en>Cuzkatzimhut: /* The logarithm of a non-diagonalizable matrix */ Mercator series link

2012-08-29T19:56:47Z

The logarithm of a non-diagonalizable matrix: Mercator series link

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Greetings! I am Myrtle Shroyer. Her husband and her reside in Puerto Rico but she will have to move one working day or an additional. I utilized to be unemployed but now I am a librarian and the salary has been really fulfilling. To gather badges is what her family members and her appreciate.<br><br>Feel free to visit my weblog :: [http://www.dhspoteh.co.kr/xe/index.php?document_srl=331302&mid=Sports std home test]