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| {{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]) |
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| In [[mathematics]], a '''nonnegative matrix''' is a [[matrix (mathematics)|matrix]] in which all the elements are equal to or greater than zero
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| : <math>\mathbf{X} \geq 0, \qquad \forall i,j\, x_{ij} \geq 0.</math>
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| 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.
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| Any [[transition matrix]] for a [[Markov chain]] is a non-negative matrix.
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| A rectangular non-negative matrix can be approximated by a decomposition with two other non-negative matrices via [[non-negative matrix factorization]].
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| A positive matrix is not the same as a [[positive-definite matrix]].
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| A matrix that is both non-negative and positive semidefinite is called a '''doubly non-negative matrix'''.
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| Eigenvalues and eigenvectors of square positive matrices are described by the [[Perron–Frobenius theorem]].
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| == Inversion ==
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| 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]].
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| 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>
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| == Specializations ==
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| 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.
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| == See also ==
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| [[Metzler matrix]]
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| == Bibliography ==
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| # Abraham Berman, Robert J. Plemmons, ''Nonnegative Matrices in the Mathematical Sciences'', 1994, SIAM. ISBN 0-89871-321-8.
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| #A. Berman and R. J. Plemmons, ''Nonnegative Matrices in the Mathematical Sciences'', Academic Press, 1979 (chapter 2), ISBN 0-12-092250-9
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| #R.A. Horn and C.R. Johnson, ''Matrix Analysis'', Cambridge University Press, 1990 (chapter 8).
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| # {{cite book| last = Krasnosel'skii
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| | first = M. A.
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| | authorlink = Mark Krasnosel'skii
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| | title=Positive Solutions of Operator Equations
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| | publisher=P.Noordhoff Ltd
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| | location= [[Groningen (city)|Groningen]]
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| | year=1964| pages=381 pp.}}
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| #{{cite book| last1 = Krasnosel'skii
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| | first1 = M. A.
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| | authorlink1=Mark Krasnosel'skii
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| | last2 = Lifshits
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| | first2 = Je.A.
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| | last3 = Sobolev
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| | first3 = A.V.
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| | title = Positive Linear Systems: The method of positive operators
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| | series = Sigma Series in Applied Mathematics | volume=5 |pages=354 pp.
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| | publisher = Helderman Verlag
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| | location= [[Berlin]]
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| | year=1990}}
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| # Henryk Minc, ''Nonnegative matrices'', John Wiley&Sons, New York, 1988, ISBN 0-471-83966-3
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| # 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
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| # [[Richard S. Varga]] 2002 ''Matrix Iterative Analysis'', Second ed. (of 1962 Prentice Hall edition), Springer-Verlag.
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| [[Category:Matrices]]
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| {{Linear-algebra-stub}}
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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.
Feel free to surf to my web page psychic phone (Www.Prograd.Uff.br)