Canonical quantum gravity - Revision history

20.133.1.1: /* Canonical quantization with constraints */ Poisson! and not Poission or Poison

2014-12-23T11:00:33Z

Canonical quantization with constraints: Poisson! and not Poission or Poison

← Older revision		Revision as of 13:00, 23 December 2014
Line 1:		Line 1:
	~~{{hatnote\|Not to be confused with [[Totally positive matrix]] and [[Positive-definite matrix]].}}~~		The writer's name is Christy Brookins. Mississippi is exactly where his home is. Distributing production is exactly where her primary income arrives from. The preferred pastime for him and his kids is to perform lacross and he would by no means give it up.<br><br>Feel free to surf to my web page psychic phone ([http://Www.Prograd.Uff.br/novo/facts-about-growing-greater-organic-garden Www.Prograd.Uff.br])

	~~In [[mathematics]], a '''nonnegative matrix''~~' is ~~a [[matrix (mathematics)\|matrix]] in which all the elements are equal to or greater than zero~~
	~~: <math>\mathbf{X} \geq 0, \qquad \forall i,j\, x_{ij} \geq 0~~.~~</math>~~
	~~A '''positive matrix'''~~ is ~~a matrix in which all the elements are greater than zero~~. ~~The set of positive matrices~~ is ~~a subset of all non-negative matrices~~.

	~~Any [[transition matrix]]~~ for ~~a [[Markov chain]] is a non-negative matrix.~~

	~~A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via [[non-negative matrix factorization]].~~

	~~A positive matrix is not the same as a [[positive-definite matrix]].~~
	~~A matrix that is both non-negative~~ and ~~positive semidefinite~~ is ~~called a '''doubly non-negative matrix'''.~~

	~~Eigenvalues~~ and ~~eigenvectors of square positive matrices are described~~ by ~~the [[Perron–Frobenius theorem]].~~

	~~== Inversion ==~~
	~~The inverse of any [[Invertible matrix\|non-singular]] [[M-matrix]] is a non-negative matrix. If the non-singular M-matrix is also symmetric then~~ it ~~is called a [[Stieltjes matrix]].~~

	The inverse of a non-negative matrix is usually not non-negative. The exception is the non-negative [[monomial matrices]]: a non-negative matrix has non-negative inverse if and only if it is a (non-negative) monomial matrix. ~~Note that thus the inverse of a positive matrix is not positive or even non-negative, as positive matrices are not monomial, for dimension~~ <~~math~~>~~n > 1.~~<~~/math~~>

	~~== Specializations ==~~
	~~There are a number of groups of matrices that form specializations of non-negative matrices, e.g.~~ [~~[stochastic matrix]]; [[doubly stochastic matrix]]; [[symmetric matrix\|symmetric]] non-negative matrix~~.

	~~== See also ==~~

	~~[[Metzler matrix]]~~

	~~== Bibliography ==~~
	~~# Abraham Berman, Robert J~~. ~~Plemmons, ''Nonnegative Matrices in the Mathematical Sciences'', 1994, SIAM~~. ~~ISBN 0~~-~~89871~~-~~321~~-8.
	~~#A. Berman and R. J. Plemmons, ''Nonnegative Matrices in the Mathematical Sciences'', Academic Press, 1979 (chapter 2), ISBN 0~~-12-~~092250-9~~
	#R.A. ~~Horn and C.R. Johnson, ''Matrix Analysis'', Cambridge University Press, 1990 (chapter 8).~~
	~~# {{cite book\| last = Krasnosel'skii~~
	~~\| first = M. A.~~
	~~\| authorlink = Mark Krasnosel'skii~~
	~~\| title=Positive Solutions of Operator Equations~~
	~~\| publisher=P~~.~~Noordhoff Ltd~~
	~~\| location= [[Groningen (city)\|Groningen]]~~
	~~\| year=1964\| pages=381 pp.}}~~
	~~#{{cite book\| last1 = Krasnosel'skii~~
	~~\| first1 = M. A.~~
	~~\| authorlink1=Mark Krasnosel'skii~~
	~~\| last2 = Lifshits~~
	~~\| first2 = Je.A.~~
	~~\| last3 = Sobolev~~
	~~\| first3 = A.V.~~
	~~\| title = Positive Linear Systems: The method of positive operators~~
	~~\| series = Sigma Series in Applied Mathematics \| volume=5 \|pages=354 pp.~~
	~~\| publisher = Helderman Verlag~~
	~~\| location= [[Berlin]]~~
	~~\| year=1990}}~~
	~~# Henryk Minc, ''Nonnegative matrices'', John Wiley&Sons, New York, 1988, ISBN 0-471-83966-3~~
	# Seneta, E. ''Non-negative matrices and Markov chains''. 2nd rev. ed., 1981, XVI, 288 p., Softcover Springer Series in Statistics. (Originally published by Allen & Unwin Ltd., London, 1973) ISBN 978-0-387-29765-1
	~~# [[Richard S. Varga~~]~~] 2002 ''Matrix Iterative Analysis'', Second ed. (of 1962 Prentice Hall edition~~)~~, Springer-Verlag.~~

	~~[[Category:Matrices]]~~


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

en>Michael Hardy at 05:22, 4 April 2013

2013-04-04T05:22:58Z

← Older revision		Revision as of 07:22, 4 April 2013
Line 1:		Line 1:
	~~Wilber Berryhill is what his wife enjoys~~ to ~~contact him~~ and ~~he totally loves this title~~. ~~Office supervising~~ is ~~what she does for~~ a ~~residing~~. The ~~favorite pastime~~ for ~~him~~ and ~~his children~~ is ~~to play lacross~~ and ~~he would~~ by ~~no means give~~ it up. ~~Kentucky~~ is ~~exactly where I've~~ usually ~~been living~~.<br><br>~~Feel free to visit my page~~ - ~~cheap psychic readings~~ ([~~http~~:~~//www~~.~~chk~~.~~woobi~~.co.~~kr/xe/?document_srl=346069 just click the following post~~])		{{hatnote\|Not to be confused with [[Totally positive matrix]] and [[Positive-definite matrix]].}}

			In [[mathematics]], a '''nonnegative matrix''' is a [[matrix (mathematics)\|matrix]] in which all the elements are equal to or greater than zero
			: <math>\mathbf{X} \geq 0, \qquad \forall i,j\, x_{ij} \geq 0.</math>
			A '''positive matrix''' is a matrix in which all the elements are greater than zero. The set of positive matrices is a subset of all non-negative matrices.

			Any [[transition matrix]] for a [[Markov chain]] is a non-negative matrix.

			A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via [[non-negative matrix factorization]].

			A positive matrix is not the same as a [[positive-definite matrix]].
			A matrix that is both non-negative and positive semidefinite is called a '''doubly non-negative matrix'''.

			Eigenvalues and eigenvectors of square positive matrices are described by the [[Perron–Frobenius theorem]].

			== Inversion ==
			The inverse of any [[Invertible matrix\|non-singular]] [[M-matrix]] is a non-negative matrix. If the non-singular M-matrix is also symmetric then it is called a [[Stieltjes matrix]].

			The inverse of a non-negative matrix is usually not non-negative. The exception is the non-negative [[monomial matrices]]: a non-negative matrix has non-negative inverse if and only if it is a (non-negative) monomial matrix. Note that thus the inverse of a positive matrix is not positive or even non-negative, as positive matrices are not monomial, for dimension <math>n > 1.</math>

			== Specializations ==
			There are a number of groups of matrices that form specializations of non-negative matrices, e.g. [[stochastic matrix]]; [[doubly stochastic matrix]]; [[symmetric matrix\|symmetric]] non-negative matrix.

			== See also ==

			[[Metzler matrix]]

			== Bibliography ==
			# Abraham Berman, Robert J. Plemmons, ''Nonnegative Matrices in the Mathematical Sciences'', 1994, SIAM. ISBN 0-89871-321-8.
			#A. Berman and R. J. Plemmons, ''Nonnegative Matrices in the Mathematical Sciences'', Academic Press, 1979 (chapter 2), ISBN 0-12-092250-9
			#R.A. Horn and C.R. Johnson, ''Matrix Analysis'', Cambridge University Press, 1990 (chapter 8).
			# {{cite book\| last = Krasnosel'skii
			\| first = M. A.
			\| authorlink = Mark Krasnosel'skii
			\| title=Positive Solutions of Operator Equations
			\| publisher=P.Noordhoff Ltd
			\| location= [[Groningen (city)\|Groningen]]
			\| year=1964\| pages=381 pp.}}
			#{{cite book\| last1 = Krasnosel'skii
			\| first1 = M. A.
			\| authorlink1=Mark Krasnosel'skii
			\| last2 = Lifshits
			\| first2 = Je.A.
			\| last3 = Sobolev
			\| first3 = A.V.
			\| title = Positive Linear Systems: The method of positive operators
			\| series = Sigma Series in Applied Mathematics \| volume=5 \|pages=354 pp.
			\| publisher = Helderman Verlag
			\| location= [[Berlin]]
			\| year=1990}}
			# Henryk Minc, ''Nonnegative matrices'', John Wiley&Sons, New York, 1988, ISBN 0-471-83966-3
			# Seneta, E. ''Non-negative matrices and Markov chains''. 2nd rev. ed., 1981, XVI, 288 p., Softcover Springer Series in Statistics. (Originally published by Allen & Unwin Ltd., London, 1973) ISBN 978-0-387-29765-1
			# [[Richard S. Varga]] 2002 ''Matrix Iterative Analysis'', Second ed. (of 1962 Prentice Hall edition), Springer-Verlag.

			[[Category:Matrices]]


			{{Linear-algebra-stub}}

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-10T16:42:39Z

ISBNs (Build KE)

New page

Wilber Berryhill is what his wife enjoys to contact him and he totally loves this title. Office supervising is what she does for a residing. The favorite pastime for him and his children is to play lacross and he would by no means give it up. Kentucky is exactly where I've usually been living.<br><br>Feel free to visit my page - cheap psychic readings ([http://www.chk.woobi.co.kr/xe/?document_srl=346069 just click the following post])