Delta set - Revision history

en>Mark viking: Added wl

2014-10-07T00:45:47Z

Added wl

← Older revision		Revision as of 02:45, 7 October 2014
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	In [~~[mathematics]~~], ~~a '''definite quadratic form'''~~ is ~~a [[quadratic form]] over some [[Real number\|real]] [[vector space]] {{math\|''V''}}~~ that ~~has~~ the ~~same [[positive~~ and ~~negative numbers\|sign]] (always positive or always negative) for every nonzero vector of {{math\|''V''}}. According~~ to that ~~sign~~, the ~~quadratic form is called '''positive definite''' or '''negative definite'~~''.		Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. It is used by around 25% of all new websites, and there are more than 27 thousand plugins currently available. If you have any questions pertaining to where and how you can utilize [http://zpib.com/wordpress_backup_373391 wordpress backup], you could call us at our web site. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. If you are happy with your new look then click "Activate 'New Theme'" in the top right corner. <br><br>

	~~A '''semidefinite''' (or '''semi~~-~~definite''') quadratic form~~ is ~~defined in~~ the ~~same way, except that "positive"~~ and ~~"negative"~~ are ~~replaced by "not negative"~~ and ~~"not positive", respectively. An '''indefinite''' quadratic form~~ is ~~one that takes on both positive and negative values.~~		As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. After all, Word - Press is free, many of the enhancements for Word - Press like themes and plugins are also free, and there is plenty of free information online about how to use Word - Press. It allows Word - Press users to easily use HTML5 the element enable native video playback within the browser. This is identical to doing a research as in depth above, nevertheless you can see various statistical details like the number of downloads and when the template was not long ago updated. This can be done by using a popular layout format and your unique Word - Press design can be achieved in other elements of the blog. <br><br>Minor and medium sized corporations also have a lot to obtain by shelling out in a very good website. Note: at a first glance WP Mobile Pro themes do not appear to be glamorous or fancy. You've got invested a great cope of time developing and producing up the topic substance. The first thing you need to do is to choose the right web hosting plan. Search engine optimization pleasant picture and solution links suggest you will have a much better adjust at gaining considerable natural site visitors. <br><br>Google Maps Excellent navigation feature with Google Maps and latitude, for letting people who have access to your account Latitude know exactly where you are. And, that is all the opposition events with nationalistic agenda in favor of the individuals of Pakistan marching collectively in the battle in opposition to radicalism. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Word - Press is the most popular open source content management system (CMS) in the world today. Digital digital cameras now function gray-scale configurations which allow expert photographers to catch images only in black and white. <br><br>You will know which of your Word - Press blog posts are attracting more unique visitors which in turn will help you develop better products and services for your customers. By using Word - Press MLM websites or blogs, an online presence for you and your MLM company can be created swiftly and simply. Must being, it's beneficial because I don't know about you, but loading an old website on a mobile, having to scroll down, up, and sideways' I find links being clicked and bounced around like I'm on a freaking trampoline. Word - Press is the most popular personal publishing platform which was launched in 2003. Press CTRL and the numbers one to six to choose your option.

	~~More generally, the definition applies~~ to ~~a vector space over an [[ordered field]]~~.~~<ref>Milnor & Husemoller (1973) p.61</ref>~~

	~~==Associated symmetric bilinear form==~~
	~~Quadratic forms correspond in one~~-to~~-one way to [[symmetric bilinear form]]s over~~ the ~~same space~~. ~~A symmetric bilinear form~~ is ~~also described~~ as ~~definite~~, ~~semidefinite, etc~~. ~~according to its associated quadratic form. A quadratic form {{math\|''Q''}}~~ and ~~its associated symmetric bilinear form {{math\|''B''}} are related by~~ the ~~following equations:~~

	:<~~math~~>~~\, Q(x) = B(x,x)~~ <~~/math~~>
	:~~<math>\, B(x,y) = B(y,x) = \tfrac{1}{2} (Q(x + y) - Q(x) - Q(y)) </math>~~

	~~==Example==~~
	~~As an example, let {{math\|1=~~'~~'V'' = ℝ<sup>2</sup>}},~~ and ~~consider~~ the ~~quadratic form~~
	~~:<math>Q(x)=c_1{x_1}^2+c_2{x_2}^2 \,</math>~~
	~~where {{math\|1=''x'' = (''x''<sub>1</sub>, ''x''<sub>2</sub>)}}~~ and ~~{{math\|''c''~~<~~sub~~>1<~~/sub~~>}} and ~~{{math\|''c''<sub>2</sub>}}~~ are ~~constants~~. ~~If {{math\|1=''c''<sub>1</sub> > 0}} and {{math\|1=''c''<sub>2</sub> > 0}}~~, the ~~quadratic form {{math\|''Q''}} is positive definite~~. ~~If one of~~ the ~~constants is positive and~~ the ~~other~~ is ~~zero, then {{math\|''Q''}}~~ is ~~positive semidefinite~~. ~~If {{math\|1=''c''~~<~~sub~~>1<~~/sub~~> ~~> 0}}~~ and ~~{{math\|1=~~''~~c''<sub>2</sub> < 0}}~~, ~~then {{math\|~~''~~Q''}} is indefinite~~.

	~~==See also==~~
	*[[Anisotropic quadratic form]]
	*[[Positive definite function]]
	*[[Positive definite matrix]]

	~~==References==~~
	~~{{reflist}}~~
	* Nathanael Leedom Ackerman (2006) [http://math.berkeley.edu/~nate/teaching/UPenn/2006/fall/math_371/lectures/week_3/lecture_4/lecture_4.pdf Lecture notes Math 371], Positive definite bilinear form is ~~definition 0~~.~~5.0.7, weblink from [[University of California, Berkeley]].~~
	* {{cite book \| last=Kitaoka \| first=Yoshiyuki \| title=Arithmetic of quadratic forms \| series=Cambridge Tracts in Mathematics \| volume=106 \| publisher=Cambridge University Press ~~\| year=1993 \| isbn=0-521-40475-4 \| zbl=0785.11021 }}~~
	* {{Lang Algebra \| edition=3r2004\|page=578}}
	* {{cite book \| first1=J. \| last1=Milnor \| author1-link=John Milnor\| first2=D. \| last2=Husemoller \| title=Symmetric Bilinear Forms \| series=[[Ergebnisse der Mathematik und ihrer Grenzgebiete]] \| volume=73 \| publisher=[[Springer-Verlag]] \| year=1973 \| isbn=3-540-06009-X \| zbl=0292.10016 }}

	~~[[Category:Quadratic forms]]~~
	~~[[Category:Linear algebra]]~~

	~~{{algebra-stub}}~~

en>ChrisGualtieri: General Fixes + MOS + DMY changes, added orphan tag using AWB

2013-07-04T14:39:12Z

General Fixes + MOS + DMY changes, added orphan tag using AWB

← Older revision		Revision as of 16:39, 4 July 2013
Line 1:		Line 1:
	~~My name is Gary McVicars but everybody calls me Gary. I~~'~~m from Austria. I~~'m studying at the high school (final year) and I play the French Horn for 10 years. Usually I choose songs from the famous films ;). <br>I have two brothers. I like American football, watching movies and Skiing.<br>xunjie まばゆいばかりの明るい鮮やかな光で出破裂コレクションは、		In [[mathematics]], a '''definite quadratic form''' is a [[quadratic form]] over some [[Real number\|real]] [[vector space]] {{math\|''V''}} that has the same [[positive and negative numbers\|sign]] (always positive or always negative) for every nonzero vector of {{math\|''V''}}. According to that sign, the quadratic form is called '''positive definite''' or '''negative definite'''.
	~~巧みに設計された改良された真空バッグがある限り、~~
	~~!クール美夏美バッグを連れて行ってあげるモンティーホール流行レースの花手受領書肩バッグ简洁大気の一种のバッグ、~~ [~~http://www.mazz.ch/windowset/r/best/chanel.html ��ͥ� �Хå� ��ӥ��~~] ~~男性と女性の天使聞いて大天使ガブリエルをプレイしても、~~
	~~繊維機器の様々なニーズを満たすために供給することができる。~~
	~~彼らの最初の販売店を構築するために、~~ [~~http://www.muss.com/js/li/good/gucci.php ��ͥ� ؔ��~~] ~~そして祖国に奉仕！~~ [~~グローバル靴網近年、~~
	~~米国のソブリン債の信用格付けをカットすることで、~~
	~~予想価格：HK $ 12,000,000-18,000,000 / USD 1,500,000-2,250,000）を見つけるのは難しい上に落ちる、~~[~~http://www.otto-weibel.ch/media/nobs/header/shop/celine/ celine ؔ�� ǥ��`��~~] ~~このウールコートの魅力である、~~
	~~ファッショニスタに必要な資金OHカジュアルなスタイルのデザインの貴族の味、~~
	~~財の生産とティファニーが遅開始したことを主張していることを理由に、~~
	~~および他の多くの大きなオフィスを持っていた。~~ [~~http://www~~.~~muss~~.~~com/js/li/good/gucci.php �ĥ�<br><br>�� ؔ��]~~

	~~Visit my page~~ - [http://~~anghaeltacht~~.~~net~~/~~ctg~~/~~cocog~~/p/~~top~~/~~gaga~~/ ~~ガガミラノ時計メンズ新作~~]		A '''semidefinite''' (or '''semi-definite''') quadratic form is defined in the same way, except that "positive" and "negative" are replaced by "not negative" and "not positive", respectively. An '''indefinite''' quadratic form is one that takes on both positive and negative values.

			More generally, the definition applies to a vector space over an [[ordered field]].<ref>Milnor & Husemoller (1973) p.61</ref>

			==Associated symmetric bilinear form==
			Quadratic forms correspond in one-to-one way to [[symmetric bilinear form]]s over the same space. A symmetric bilinear form is also described as definite, semidefinite, etc. according to its associated quadratic form. A quadratic form {{math\|''Q''}} and its associated symmetric bilinear form {{math\|''B''}} are related by the following equations:

			:<math>\, Q(x) = B(x,x) </math>
			:<math>\, B(x,y) = B(y,x) = \tfrac{1}{2} (Q(x + y) - Q(x) - Q(y)) </math>

			==Example==
			As an example, let {{math\|1=''V'' = ℝ<sup>2</sup>}}, and consider the quadratic form
			:<math>Q(x)=c_1{x_1}^2+c_2{x_2}^2 \,</math>
			where {{math\|1=''x'' = (''x''<sub>1</sub>, ''x''<sub>2</sub>)}} and {{math\|''c''<sub>1</sub>}} and {{math\|''c''<sub>2</sub>}} are constants. If {{math\|1=''c''<sub>1</sub> > 0}} and {{math\|1=''c''<sub>2</sub> > 0}}, the quadratic form {{math\|''Q''}} is positive definite. If one of the constants is positive and the other is zero, then {{math\|''Q''}} is positive semidefinite. If {{math\|1=''c''<sub>1</sub> > 0}} and {{math\|1=''c''<sub>2</sub> < 0}}, then {{math\|''Q''}} is indefinite.

			==See also==
			*[[Anisotropic quadratic form]]
			*[[Positive definite function]]
			*[[Positive definite matrix]]

			==References==
			{{reflist}}
			* Nathanael Leedom Ackerman (2006) [http://math.berkeley.edu/~nate/teaching/UPenn/2006/fall/math_371/lectures/week_3/lecture_4/lecture_4.pdf Lecture notes Math 371], Positive definite bilinear form is definition 0.5.0.7, weblink from [[University of California, Berkeley]].
			* {{cite book \| last=Kitaoka \| first=Yoshiyuki \| title=Arithmetic of quadratic forms \| series=Cambridge Tracts in Mathematics \| volume=106 \| publisher=Cambridge University Press \| year=1993 \| isbn=0-521-40475-4 \| zbl=0785.11021 }}
			* {{Lang Algebra \| edition=3r2004\|page=578}}
			* {{cite book \| first1=J. \| last1=Milnor \| author1-link=John Milnor\| first2=D. \| last2=Husemoller \| title=Symmetric Bilinear Forms \| series=[[Ergebnisse der Mathematik und ihrer Grenzgebiete]] \| volume=73 \| publisher=[[Springer-Verlag]] \| year=1973 \| isbn=3-540-06009-X \| zbl=0292.10016 }}

			[[Category:Quadratic forms]]
			[[Category:Linear algebra]]

			{{algebra-stub}}

en>Gabbe: /* References */ changed to character entity references to avoid display being mangled

2012-08-30T12:03:45Z

References: changed to character entity references to avoid display being mangled

New page

My name is Gary McVicars but everybody calls me Gary. I'm from Austria. I'm studying at the high school (final year) and I play the French Horn for 10 years. Usually I choose songs from the famous films ;). <br>I have two brothers. I like American football, watching movies and Skiing.<br>xunjie まばゆいばかりの明るい鮮やかな光で出破裂コレクションは、
巧みに設計された改良された真空バッグがある限り、
!クール美夏美バッグを連れて行ってあげるモンティーホール流行レースの花手受領書肩バッグ简洁大気の一种のバッグ、 [http://www.mazz.ch/windowset/r/best/chanel.html ��ͥ� �Хå� ��ӥ��] 男性と女性の天使聞いて大天使ガブリエルをプレイしても、
繊維機器の様々なニーズを満たすために供給することができる。
彼らの最初の販売店を構築するために、 [http://www.muss.com/js/li/good/gucci.php ��ͥ� ؔ��] そして祖国に奉仕！ [グローバル靴網近年、
米国のソブリン債の信用格付けをカットすることで、
予想価格：HK $ 12,000,000-18,000,000 / USD 1,500,000-2,250,000）を見つけるのは難しい上に落ちる、[http://www.otto-weibel.ch/media/nobs/header/shop/celine/ celine ؔ�� ǥ��`��] このウールコートの魅力である、
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財の生産とティファニーが遅開始したことを主張していることを理由に、
および他の多くの大きなオフィスを持っていた。 [http://www.muss.com/js/li/good/gucci.php �ĥ�<br><br>�� ؔ��]

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