Pascal matrix - Revision history

en>Rjwilmsi: /* References */Added 1 doi to a journal cite using AWB (10222)

2014-06-08T13:49:21Z

References: Added 1 doi to a journal cite using AWB (10222)

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	~~{{dablink\|For the [[chemistry]] related meaning of this term see [[Z-matrix (chemistry)]].}}~~		Hello, my name is Andrew and my wife doesn't like it at all. For a while I've been in Mississippi but now I'm considering other choices. He functions as a bookkeeper. To climb is some thing I truly appreciate performing.<br><br>my web blog are psychics real ([http://cpacs.org/index.php?document_srl=90091&mid=board_zTGg26 cpacs.org])

	~~In [[mathematics]]~~, ~~the class of ''Z''-matrices are those [[matrix (mathematics)\|matrices]] whose off-diagonal entries are less than or equal to zero; that~~ is~~, a~~ '~~'Z''-matrix ''Z'' satisfies~~

	~~:<math>Z=(z_{ij});\quad z_{ij}\leq 0, \quad i\neq j~~.~~</math>~~

	~~Note that this definition coincides precisely with that of~~ a '~~''negated''' [[Metzler matrix]] or [[quasipositive matrix]], thus the term ''quasinegative'' matrix appears from time to time in the literature, though this is rare and usually only~~ in ~~contexts where references to quasipositive matrices are made.~~

	~~The [[Jacobian matrix and determinant\|Jacobian]] of a~~ '~~''competitive''' dynamical system is a ''Z''-matrix by definition~~. ~~Likewise, if the Jacobian of a '''cooperative''' dynamical system is ''J'', then (−''J'') is~~ a ~~''Z''-matrix~~.

	Related classes are [[L-matrix\|''L''-matrices]], [[M-matrix\|''M''-matrices]], [[P-matrix \| ''P''-matrices]], [[Hurwitz matrix \| ''Hurwitz'' matrices]] and [[Metzler matrix \|''Metzler'' matrices]]. ''L''-matrices have the additional property that all diagonal entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a ''Z''-matrix is an ''M''-matrix if it is ~~[[nonsingular]] and its inverse is nonnegative~~. ~~All matrices that~~ are ~~both ''Z''-matrices and [~~[~~P-matrix\|''P''-matrices]] are nonsingular ''M''-matrices.~~

	~~==See also==~~
	* [[P-matrix]]
	* [[M-matrix]]
	* [[Hurwitz matrix]]
	* [[Metzler matrix]]

	~~== References ==~~

	* {{cite journal\| doi= 10.1016/j.amc.2005.07.050\| author=Huan T., Cheng G., Cheng X.\| title= Modified SOR-type iterative method for Z-matrices\|journal = Applied Mathematics and Computation\| volume =175 \|issue =1\|date= 1 April 2006\| pages= 258–268}}
	* {{cite book \| url=http://~~www-users.cs.umn~~.~~edu~~/~~~saad/books~~.~~html\|author~~= ~~Saad, Y. \|title~~=~~Iterative methods for sparse linear systems\| publisher= Society for Industrial and Applied Mathematics\|location= Philadelphia, PA~~.~~\|edition =2nd \| page =28 \| isbn=0-534-94776-X}}~~

	~~[[Category:Matrices~~]]


	~~{{Linear-algebra-stub}}~~

en>Monkbot: /* References */Fix CS1 deprecated date parameter errors

2014-01-28T05:33:37Z

References: Fix CS1 deprecated date parameter errors

← Older revision		Revision as of 07:33, 28 January 2014
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	~~fee to watch your webinar at their convenience.~~ For ~~more in regards to~~ [~~http://ganhedinheironainternet.comoganhardinheiro101.com como ganhar dinheiro na internet~~] ~~have a look at http://ganhedinheironainternet.comoganhardinheiro101.com Once it is in place,~~ [~~http://www.comoganhardinheiro101.com/testemunhos/ como conseguir dinheiro~~] ~~promotion and possibly answering questions will be your only tasks~~. ~~<br><br><br>~~		{{dablink\|For the [[chemistry]] related meaning of this term see [[Z-matrix (chemistry)]].}}

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			:<math>Z=(z_{ij});\quad z_{ij}\leq 0, \quad i\neq j.</math>

			Note that this definition coincides precisely with that of a '''negated''' [[Metzler matrix]] or [[quasipositive matrix]], thus the term ''quasinegative'' matrix appears from time to time in the literature, though this is rare and usually only in contexts where references to quasipositive matrices are made.

			The [[Jacobian matrix and determinant\|Jacobian]] of a '''competitive''' dynamical system is a ''Z''-matrix by definition. Likewise, if the Jacobian of a '''cooperative''' dynamical system is ''J'', then (−''J'') is a ''Z''-matrix.

			Related classes are [[L-matrix\|''L''-matrices]], [[M-matrix\|''M''-matrices]], [[P-matrix \| ''P''-matrices]], [[Hurwitz matrix \| ''Hurwitz'' matrices]] and [[Metzler matrix \|''Metzler'' matrices]]. ''L''-matrices have the additional property that all diagonal entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a ''Z''-matrix is an ''M''-matrix if it is [[nonsingular]] and its inverse is nonnegative. All matrices that are both ''Z''-matrices and [[P-matrix\|''P''-matrices]] are nonsingular ''M''-matrices.

			==See also==
			* [[P-matrix]]
			* [[M-matrix]]
			* [[Hurwitz matrix]]
			* [[Metzler matrix]]

			== References ==

			* {{cite journal\| doi= 10.1016/j.amc.2005.07.050\| author=Huan T., Cheng G., Cheng X.\| title= Modified SOR-type iterative method for Z-matrices\|journal = Applied Mathematics and Computation\| volume =175 \|issue =1\|date= 1 April 2006\| pages= 258–268}}
			* {{cite book \| url=http://www-users.cs.umn.edu/~saad/books.html\|author= Saad, Y. \|title=Iterative methods for sparse linear systems\| publisher= Society for Industrial and Applied Mathematics\|location= Philadelphia, PA.\|edition =2nd \| page =28 \| isbn=0-534-94776-X}}

			[[Category:Matrices]]


			{{Linear-algebra-stub}}

en>R'n'B: Fix links to disambiguation page Matrix theory

2012-07-27T23:17:41Z

Fix links to disambiguation page Matrix theory

New page

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