Polar decomposition - Revision history

en>Saung Tadashi: /* See also */ Added a link for algebraic polar decomposition

2014-12-11T22:22:30Z

See also: Added a link for algebraic polar decomposition

← Older revision		Revision as of 00:22, 12 December 2014
Line 300:		Line 300:

	<li>[http://metransparent.nfrance.com/~k1001/spip.php?article5808&lang=ar&id_forum=6858/ http://metransparent.nfrance.com/~k1001/spip.php?article5808&lang=ar&id_forum=6858/]</li>		<li>[http://metransparent.nfrance.com/~k1001/spip.php?article5808&lang=ar&id_forum=6858/ http://metransparent.nfrance.com/~k1001/spip.php?article5808&lang=ar&id_forum=6858/]</li>

			</ul>

			== Nike Free 5.0 Homme Vous pouvez ==

			Netcraft écoutes serveurs Web 48m active. Peu à peu, il y aura plus. J'ai eu le dernier problème et convaincre le gérant du magasin pour me donner 15% de rabais sur le matériel restant depuis que j'en avais besoin pour terminer le pont, mais il [http://www.hassler-solarenergie.ch/download/format.asp?show=20-Nike-Free-5.0-Homme Nike Free 5.0 Homme] wasn excité à ce sujet. <br><br>Vous pouvez, cependant, inscrivez-vous sans votre compte SYA, ou avec un autre compte que vous pourriez avoir. Contrairement à la série précédente, celle-ci n'est pas sensiblement écrit par Joss Whedon, dont le rôle en tant que créateur est plus proche de Abrams est dans un certain nombre de ses projets. <br><br>Ils ont constaté que les personnes atteintes de ces maladies ont été souvent considérés comme difficiles à parler et dans certains cas ont été considérés comme imprévisible et potentiellement violent. Vous pouvez lire des livres gratuitement en ligne avec vos enfants et vous aider les autres en le faisant. Suresh dit précautions ont été prises pour donner une sensation de classe pour le cours.<br><br>L'Internet était en proie à la spéculation toute la semaine sur les changements imminents à Facebook Fil d'actualité, qui ont été officiellement annoncées hier. Nous apprécions tous beaucoup. Lire un livre. Brad a remporté «Le Prix du Jeune Reporter de Hollywood Star» en 1995 et a été nommé comme l'un des People Magazine [http://www.lauinger.ch/images/files/frame.asp?y=180-Nike-Air-Max-Tn-Requin Nike Air Max Tn Requin] du "Top 30 Moins de 30." <br><br>Meyer a déclaré Terri lui a dit qu'elle n'était pas d'accord avec la décision bien connue par les parents Quinlan à prendre leur fille dans le coma débrancher son respirateur. Ils ont tiré [l'entraîneur de tangage]. Les astronomes amateurs, les astronomes, et les amateurs de plein air de même trouver une consolation dans ce peu de lumière, communauté peu électrifié de part haciendas de temps.<br><br>Dans les douze mois, le nouveau document a été vend mieux que The Times .. L'iPad fait d'offrir aux éditeurs la possibilité de vendre leurs livres dans des formats non propriétaires, ce qui signifie que lorsque vous souhaitez passer à un autre type de lecteur, vos livres peuvent aller avec vous.<br><br>Pour être tué. Les [http://www.vonwil.ch/literatur/psearch.asp?t=22-Bottes-Timberland-Femme Bottes Timberland Femme] prêteurs vont certainement fonder leur propre décision sur quelques variables, mais le plus important sera votre pointage de crédit. Le porc récoltés dans ces images a la plupart du temps dans soppressata, saucisse fraîche, saucisse et. Le [5] Cour suprême a statué que Glivec n'est pas nouveau, pas d'innovation et manqué à la section 3 (d) critères qui stipule que les inventions qui [http://www.seilparks.ch/downloads/mitglieder/default.asp?PAGE=143-Nike-Chaussure-De-Sport Nike Chaussure De Sport] sont un simple d'une forme d'une substance n'entraînent pas une augmentation de l'efficacité de cette substance et<ul>

			<li>[http://enseignement-lsf.com/spip.php?article64#forum17875501 http://enseignement-lsf.com/spip.php?article64#forum17875501]</li>

			<li>[http://www.theplayingbay.com/activity/p/247262/ http://www.theplayingbay.com/activity/p/247262/]</li>

			<li>[http://enseignement-lsf.com/spip.php?article65#forum17865468 http://enseignement-lsf.com/spip.php?article65#forum17865468]</li>

			<li>[http://www.oisex.cn/forum.php?mod=viewthread&tid=666016 http://www.oisex.cn/forum.php?mod=viewthread&tid=666016]</li>

			<li>[http://lmusicradio.altervista.org/osclass/index.php?page=item&id=74624 http://lmusicradio.altervista.org/osclass/index.php?page=item&id=74624]</li>

	</ul>		</ul>

en>BG19bot: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{2 → ² (2) using AWB (9957)}

2014-03-01T08:45:02Z

WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: 2 → 2 (2) using AWB (9957)

Show changes

en>Noix07: /* Bounded operators on Hilbert space */

2013-12-16T20:23:56Z

Bounded operators on Hilbert space

← Older revision		Revision as of 22:23, 16 December 2013
Line 1:		Line 1:
	The name of the ~~writer~~ is ~~Garland~~. ~~Bookkeeping~~ is ~~what she does~~. The ~~preferred pastime~~ for ~~him~~ and ~~his kids~~ is to ~~perform badminton~~ but he is ~~having difficulties~~ to ~~discover time~~ for it. ~~Delaware~~ is ~~our birth~~ place.<br><br>~~Visit my page~~ ... [http://~~Www~~.~~Igearclearance~~.~~com~~/~~UserProfile~~/~~tabid~~/~~143/userId/157989/Default~~.~~aspx auto warranty~~]		{{original_research\|date=February 2013}}
			[[Image:M2VelocityEMratioUS052009.png\|300px\|thumb\|Chart showing the log of US M2<ref>[http://www.investopedia.com/terms/m/m2.asp M2 Definition] – Investopedia</ref><ref>[http://research.stlouisfed.org/fred2/series/M2 M2 Money Stock] – Federal Reserve Bank of St Louis</ref> money velocity (green), calculated by dividing nominal GDP by M2 stock, M1 plus [[time deposit]]s 1959–2010. [[Employment-to-population ratio]] is displayed in blue, and periods of recession are represented with gray bars).]]
			[[Image:M1VelocityEMratioUS052009.png\|300px\|thumb\|Similar chart showing the velocity of a slightly narrower measure of money consisting of currency and liquid deposits M1 1959–2010.]]
			[[image:M3 Velocity in the US.png\|300px\|thumb\|Similar chart showing the velocity of a broader measure of money that covers M2 plus large institutional deposits, M3. The US no longer publishes official M3 measures, so the chart only runs through 2005.]]

			The '''velocity of money''' (also called '''velocity of circulation of money''' and, much earlier, '''currency''') is the [[frequency]] at which one unit of currency is used to purchase domestically-produced goods and services within a given time period.<ref name="fred2m2v">{{cite web \| title = Money Velocity \| publisher = Federal Reserve Bank of St. Louis \| date = \| url = http://research.stlouisfed.org/fred2/series/M2V \| accessdate = October 28, 2013}}</ref> In other words, it is the number of times one dollar is spent to buy goods and services per unit of time.<ref name="fred2m2v"/> If the velocity of money is increasing, then more transactions are occurring between individuals in an economy.<ref name="fred2m2v"/> Although once thought to be constant{{citation needed\|date=October 2013}}, it is now understood that the velocity of money changes over time and is influenced by a variety of factors.<ref>Mishkin, Frederic S. ''The Economics of Money, Banking, and Financial Markets''. Seventh Edition. Addison–Wesley. 2004. p.520.</ref>

			When the period is understood, the velocity may be presented as a pure number; otherwise it should be given as a pure number divided by time.{{citation needed\|date=October 2013}}

			== Illustration ==

			If, for example, in a very small economy, a [[farmer]] and a [[mechanic]], with just $50 between them, buy new goods and services from each other in just three transactions over the course of a year
			*Farmer spends $50 on [[tractor]] repair from mechanic.
			*Mechanic buys $40 of [[Maize\|corn]] from farmer.
			*Mechanic spends $10 on [[Farm_cat\|barn cats]] from farmer.
			then $100 changed hands in the course of a year, even though there is only $50 in this little economy. That $100 level is possible because each dollar was spent on new goods and services an average of twice a year, which is to say that the velocity was <math>2/\text{year}</math>. Note that if the farmer bought a used tractor from the mechanic or made a gift to the mechanic, it would not go into the numerator of velocity because that transaction would not be part of this tiny economy's gross domestic product.

			== Indirect measurement ==

			In practice, attempts to measure the velocity of money are usually indirect:
			:<math>V_T =\frac{nT}{M}</math>
			where
			:<math>V_T\,</math> is the velocity of money for all transactions in a given time frame.
			:<math>nT\,</math> is the [[Real versus nominal value (economics)\|nominal value]] of aggregate transactions in a given time frame.
			:<math>M\,</math> is the total amount of [[money supply\|money]] in circulation on average in the economy (see “[[Money supply]]” for details).

			(Given the [[classical dichotomy]], <math>nT</math> may be factored into a product <math>P\cdot T</math> of a [[price level]] <math>P</math> and a '[[Real versus nominal value (economics)\|real]]' aggregate value of transactions <math>T</math>.)

			Values of <math>nT</math> and <math>M</math> permit calculation of <math>V_T</math>.

			As applied to an economy, expenditures on final output are of interest; the relation may be written:
			:<math>V =\frac{nQ}{M}</math>
			where
			:<math>V\,</math> is the velocity for transactions counting towards [[measures of national income and output\|national or domestic product]].
			:<math>nQ\,</math> is nominal [[measures of national income and output\|national or domestic product]].
			(Analogously with <math>nT</math>, given the [[classical dichotomy]], <math>nQ</math> may be factored into a product <math>P\cdot Q</math>.)

			<center><gallery>
			File:Velocity of M1 Money Stock in the US.png\|Velocity of M1 Money Stock in the US 1959–2012
			File:Velocity of M2 Money Stock in the US.png\|Velocity of M2 Money Stock in the US 1959–2012
			File:Velocity of MZM Money Stock in the US.png\|Velocity of MZM Money Stock in the US 1959–2012
			</gallery></center>

			== Determination ==

			The determinants and consequent stability of the velocity of money are a subject of controversy across and within [[economic schools of thought\|schools of economic thought]]. Those favoring a [[quantity theory of money]] have tended to believe that, in the absence of [[inflation]]ary or [[deflation]]ary expectations, velocity will be technologically determined and stable, and that such expectations will not generally arise without a signal that overall prices have changed or will change. This view has been discredited by the precipitous fall in velocity in the Japanese "Lost Decade" and the worldwide "Great Recession" and its aftermath of 2008–10. Monetary authorities undertook massive expansion of the money supplies, but instead of lifting nominal GDP as predicted by this theory, velocity fell as nominal GDP was relatively unchanged.{{citation_needed\|date=February 2013}}

			Some people have incorrectly interpreted velocity to mean the time between receipt of income and when it is spent. Note that how much income is spent helps determine GDP, but the time during a pay period at which it is spent is immaterial. There could be a large volume of spending by people who waited a long time between receiving income and spending it. They could store their income in non-money forms, such as stocks and bonds, between receiving income and spending it. So the notion that velocity of money equates to "how fast income is spent" is a fallacy.{{citation_needed\|date=February 2013}}

			The view that velocity of money is constant is criticized by [[Paul Samuelson\|Samuelson]] thus:
			{{Quotation\|In terms of the quantity theory of money, we may say that the velocity of circulation of money does not remain constant. “You can lead a horse to water, but you can’t make him drink.” You can force money on the system in exchange for government bonds, its close money substitute; but you can’t make the money circulate against new goods and new jobs.<ref name="sam_vel">Samuelson, Paul Anthony; ''Economics'' (1948), p 354.</ref>}}

			== Criticism ==

			=== Austrian school of economics ===
			[[Henry Hazlitt]] criticized the concept of the velocity of money, citing that the equation used to calculate it ignored the psychological effects that also have a significant role in determining the value of a currency. As an example, he shows that in a period of inflation, that when the money is newly introduced, the price level increases by a smaller proportion than the increase in the supply of money, but that when the money has been in circulation for a while, that the price level has increased by a greater proportion than the supply of money. He states that this is not due to a change in the velocity of money, but rather the discrepancy is due to "fears . . . that the inflation will continue into the future, and that the value of the monetary unit will fall further." Hazlitt offers an alternative to the quantity theory of money and the velocity of money concept that is a necessary consequence. He explains that what changes the value of money is the value that people place on the currency, and that it is not the velocity of money that determines the value of a currency, but rather the sum of individuals' value of the currency that determines the velocity of money. <ref>http://mises.org/daily/2916</ref>

			[[Ludwig von Mises]] offered a more philosophical criticism, "The main deficiency of the velocity of circulation concept is that it does not start from the actions of individuals but looks at the problem from the angle of the whole economic system. This concept in itself is a vicious mode of approaching the problem of prices and purchasing power. It is assumed that, other things being equal, prices must change in proportion to the changes occurring in the total supply of money available. This is not true." <ref>Ludwig von Mises, Human Action (New Haven: Yale University Press, 1949), and The Theory of Money and Credit (London: Jonathan Cape, Limited, 1934, and New Haven: Yale University Press, 1953).</ref>

			== References ==
			=== Notes ===
			{{reflist}}
			=== Sources ===
			* Cramer, J.S. “velocity of circulation”, ''[[The New Palgrave: A Dictionary of Economics]]''(1987), v. 4, pp. 601–02.
			* Friedman, Milton; “quantity theory of money”, in ''[[The New Palgrave: A Dictionary of Economics]]'' (1987), v. 4, pp. 3–20.

			== External links ==
			* [http://research.stlouisfed.org/fred2/categories/32242 Velocity of money data] – from the St. Louis Fed's FRED database

			[[Category:Monetary economics]]
			[[Category:Freiwirtschaft]]
			[[Category:Economics terminology]]

en>Rgdboer: /* Alternative planar decompositions */ ce

2012-06-30T04:07:58Z

Alternative planar decompositions: ce

New page

The name of the writer is Garland. Bookkeeping is what she does. The preferred pastime for him and his kids is to perform badminton but he is having difficulties to discover time for it. Delaware is our birth place. Visit my page ... [http://Www.Igearclearance.com/UserProfile/tabid/143/userId/157989/Default.aspx auto warranty]

Polar decomposition - Revision history

en>Saung Tadashi: /* See also */ Added a link for algebraic polar decomposition

en>BG19bot: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: 2 → 2 (2) using AWB (9957)

en>Noix07: /* Bounded operators on Hilbert space */

en>Rgdboer: /* Alternative planar decompositions */ ce

en>BG19bot: WP:CHECKWIKI error fix for #99. Broken sup tag. Do general fixes if a problem exists. -, replaced: ^{2 → ² (2) using AWB (9957)}