Himmelblau's function - Revision history

en>Bender235 at 15:16, 12 September 2014

2014-09-12T15:16:00Z

en>WQUlrich at 21:11, 25 November 2013

2013-11-25T21:11:10Z

← Older revision		Revision as of 23:11, 25 November 2013
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			In [[mathematics]] a '''single-entry matrix''' is a [[matrix (mathematics)\|matrix]] where a single element is one and the rest of the elements are zero,<ref>{{Cite web
			\| author = Kaare Brandt Petersen & Michael Syskind Pedersen
			\| title = The Matrix Cookbook
			\| date = 2008-02-16
			\| url = http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/3274/pdf/imm3274.pdf
			}}</ref><ref>{{Cite journal
			\| author = Shohei Shimizu, Patrick O. Hoyer, Aapo Hyvärinen & Antti Kerminen
			\| title = A Linear Non-Gaussian Acyclic Model for Causal Discovery
			\| journal = [[Journal of Machine Learning Research]]
			\| volume = 7
			\| year = 2006
			\| pages = 2003–2030
			\| url = http://www.cs.helsinki.fi/group/neuroinf/lingam/JMLR06.pdf
			}}</ref> e.g.,
			:<math>\mathbf{J}^{23} = \left[\begin{matrix}
			0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{matrix}\right].</math>

			It is a specific type of a [[sparse matrix]].
			The single-entry matrix can be regarded a row-selector when it is multiplied on the left side of the matrix, e.g.:
			: <math>
			\mathbf{J}^{23}\mathbf{A} = \left[ \begin{matrix} 0 & 0& 0 \\ a_{31} & a_{32} & a_{33} \\ 0 & 0 & 0 \end{matrix}\right]
			</math>
			Alternatively, a column-selector when multiplied on the right side:
			: <math>
			\mathbf{A}\mathbf{J}^{23} = \left[ \begin{matrix} 0 & 0 & a_{12} \\ 0 & 0 & a_{22} \\ 0 & 0 & a_{32} \end{matrix}\right]
			</math>

			The name, single-entry matrix, is not common, but seen in a few works.<ref>Examples:
			* {{cite web
			\| title = Distributed Gain Matrix Optimization in
			Non-Regenerative MIMO Relay Networks
			\| url = http://www.nari.ee.ethz.ch/wireless/pubs/files/asilomar09r.pdf
			}}
			* {{Cite web
			\| author = Marcel Blattner
			\| title = B-Rank: A top N Recommendation Algorithm
			\| url = http://arxiv.org/pdf/0908.2741.pdf
			}}</ref>

			==References==
			{{Reflist}}

			{{DEFAULTSORT:Single-Entry Matrix}}
			[[Category:Sparse matrices]]


			{{Linear-algebra-stub}}

en>Debivort: RV, see alsos need to be links at least

2012-02-15T16:07:45Z

RV, see alsos need to be links at least

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