Layered hidden Markov model - Revision history

en>AnomieBOT: Dating maintenance tags: {{Refimprove}}

2014-09-19T00:39:07Z

Dating maintenance tags: {{Refimprove}}

← Older revision		Revision as of 02:39, 19 September 2014
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	~~The '''invariant factors''' of a~~ [~~[module (mathematics)\|module~~]~~] over a [[principal ideal domain]] (PID) occur in one form~~ of the [~~[structure theorem for finitely generated modules over a principal ideal domain]]~~.		Let me initial start by introducing myself. My title at home [http://health.cvs.com/GetContent.aspx?token=f75979d3-9c7c-4b16-af56-3e122a3f19e3&chunkiid=21271 std testing] is Boyd Butts although it is not the title on my birth certification. Years ago we moved to North Dakota. One of the very very std testing at home best things in [http://xrambo.com/blog/192034 over the counter std test] globe home [http://www.pornextras.info/blog/187567 std home test] test kit for him is to collect badges but he is having [http://Www.Slideshare.net/realtrafficsource/celebrities-with-herpes difficulties] to find time for it. I used to be unemployed but now I am a librarian and the wage has been truly satisfying.<br><br>Also visit my homepage; [http://www.karachicattleexpo.com/blog/56 karachicattleexpo.com]

	~~If <math>R<~~/~~math> is a [[Principal ideal domain\|PID~~]~~] and <math>M</math> a [~~[~~Finitely-generated module\|finitely generated]] <math>R</math>-module, then~~

	:~~<math>M\cong R^r\oplus R~~/~~(a_1)\oplus R~~/~~(a_2)\oplus\cdots\oplus R~~/~~(a_m)<~~/~~math>~~

	for ~~some integer <math>r\geq0<~~/~~math> and a (possibly empty) list of nonzero elements <math>a_1,\ldots,a_m\in R<~~/~~math> for which <math>a_1 \mid a_2 \mid \cdots \mid a_m</math>~~. ~~The nonnegative integer <math>r</math> is called the ''free rank'' or ''Betti number'' of the module <math>M<~~/~~math>, while <math>a_1,\ldots,a_m<~~/~~math> are the ''invariant factors'' of <math>M</math> and are unique up~~ to ~~[[associatedness]]~~.

	~~The invariant factors of a [[Matrix (mathematics)\|matrix]] over~~ a ~~PID occur in the [[Smith normal form]]~~ and ~~provide a means of computing~~ the ~~structure of a module from a set of generators and relations~~.

	~~==See also==~~
	* [~~[Elementary divisors]]~~

	~~==References==~~
	* {{cite book \| author=B. ~~Hartley \| authorlink=Brian Hartley \| coauthors=T~~.O. ~~Hawkes \| title=Rings, modules and linear algebra \| publisher=Chapman and Hall \| year=1970 \| isbn=0-412-09810-5 }} Chap.8, p.128.~~
	* Chapter III.7, p.153 of {{Lang Algebra\|edition=3}}

	~~[[Category:Module theory]~~]


	~~{{Abstract-algebra-stub}}~~

en>Edward: link overfitting using Find link

2012-12-07T09:01:19Z

link overfitting using Find link

← Older revision		Revision as of 11:01, 7 December 2012
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	~~They call me Emilia~~. ~~To do aerobics~~ is a ~~factor that I'm totally addicted to. He utilized to be unemployed but now he is~~ a ~~meter reader. California is where her house is but she requirements to move simply because of her family.~~<br><br>~~My web~~-~~site; [http~~://~~www~~.~~1a-pornotube.com~~/~~blog~~/~~84958~~ over the ~~counter std test~~]		The '''invariant factors''' of a [[module (mathematics)\|module]] over a [[principal ideal domain]] (PID) occur in one form of the [[structure theorem for finitely generated modules over a principal ideal domain]].

			If <math>R</math> is a [[Principal ideal domain\|PID]] and <math>M</math> a [[Finitely-generated module\|finitely generated]] <math>R</math>-module, then

			:<math>M\cong R^r\oplus R/(a_1)\oplus R/(a_2)\oplus\cdots\oplus R/(a_m)</math>

			for some integer <math>r\geq0</math> and a (possibly empty) list of nonzero elements <math>a_1,\ldots,a_m\in R</math> for which <math>a_1 \mid a_2 \mid \cdots \mid a_m</math>. The nonnegative integer <math>r</math> is called the ''free rank'' or ''Betti number'' of the module <math>M</math>, while <math>a_1,\ldots,a_m</math> are the ''invariant factors'' of <math>M</math> and are unique up to [[associatedness]].

			The invariant factors of a [[Matrix (mathematics)\|matrix]] over a PID occur in the [[Smith normal form]] and provide a means of computing the structure of a module from a set of generators and relations.

			==See also==
			* [[Elementary divisors]]

			==References==
			* {{cite book \| author=B. Hartley \| authorlink=Brian Hartley \| coauthors=T.O. Hawkes \| title=Rings, modules and linear algebra \| publisher=Chapman and Hall \| year=1970 \| isbn=0-412-09810-5 }} Chap.8, p.128.
			* Chapter III.7, p.153 of {{Lang Algebra\|edition=3}}

			[[Category:Module theory]]


			{{Abstract-algebra-stub}}

en>ChrisGualtieri: /* The layered hidden Markov model */Typo fixing using AWB

2012-07-24T05:12:58Z

The layered hidden Markov model: Typo fixing using AWB

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