Dynamic programming: Difference between revisions

Revision as of 14:38, 15 January 2014

In mathematics, a complex square matrix U is unitary if

U^{*} U = U U^{*} = I

where I is the identity matrix and U* is the conjugate transpose of U.

The real analogue of a unitary matrix is an orthonormal matrix.

Properties

For any unitary matrix U, the following hold:

Given two complex vectors x and y, multiplication by U preserves their inner product; that is,

⟨ U x, U y ⟩ = ⟨ x, y ⟩

.

U is normal
U is diagonalizable; that is, U is unitarily similar to a diagonal matrix, as a consequence of the spectral theorem. Thus U has a decomposition of the form

U = V D V^{*}

where V is unitary and D is diagonal and unitary.

$| \det (U) | = 1$ .
Its eigenspaces are orthogonal.
For any positive integer n, the set of all n by n unitary matrices with matrix multiplication forms a group, called the unitary group U(n).
Any square matrix with unit Euclidean norm is the average of two unitary matrices.^[1]

Equivalent conditions

If U is a square, complex matrix, then the following conditions are equivalent:

U is unitary
U* is unitary
U is invertible, with U^–1=U*.
the columns of U form an orthonormal basis of $ℂ^{n}$ with respect to the usual inner product
the rows of U form an orthonormal basis of $ℂ^{n}$ with respect to the usual inner product
U is an isometry with respect to the usual norm
U is a normal matrix with eigenvalues lying on the unit circle.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

External links

I had like 17 domains hosted on single account, and never had any special troubles. If you are not happy with the service you will get your money back with in 45 days, that's guaranteed. But the Search Engine utility inside the Hostgator account furnished an instant score for my launched website. Fantastico is unable to install WordPress in a directory which already have any file i.e to install WordPress using Fantastico the destination directory must be empty and it should not have any previous installation files. When you share great information, others will take note. Once your hosting is purchased, you will need to setup your domain name to point to your hosting. Money Back: All accounts of Hostgator come with a 45 day money back guarantee. If you have any queries relating to where by and how to use Hostgator Discount Coupon, you can make contact with us at our site. If you are starting up a website or don't have too much website traffic coming your way, a shared plan is more than enough. Condition you want to take advantage of the worldwide web you prerequisite a HostGator web page, -1 of the most trusted and unfailing web suppliers on the world wide web today. Since, single server is shared by 700 to 800 websites, you cannot expect much speed.

Hostgator tutorials on how to install Wordpress need not be complicated, especially when you will be dealing with a web hosting service that is friendly for novice webmasters and a blogging platform that is as intuitive as riding a bike. After that you can get Hostgator to host your domain and use the wordpress to do the blogging. Once you start site flipping, trust me you will not be able to stop. I cut my webmaster teeth on Control Panel many years ago, but since had left for other hosting companies with more commercial (cough, cough) interfaces. If you don't like it, you can chalk it up to experience and go on. First, find a good starter template design. When I signed up, I did a search for current "HostGator codes" on the web, which enabled me to receive a one-word entry for a discount. Your posts, comments, and pictures will all be imported into your new WordPress blog.
53 yrs old Fitter (Common ) Batterton from Carp, likes to spend some time kid advocate, property developers in singapore and handball. Completed a cruise liner experience that was comprised of passing by Gusuku Sites and Related Properties of the Kingdom of Ryukyu.

Here is my web page www.mtfgaming.com

↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[1] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[1]

@@ Line 1: / Line 1: @@
-Maurice Buckles just what my wife loves to call me and I totally love this name or company name. To ride horses is something that she's been doing in most. Her family lives in Mississippi and my spouse everything she needs at this time there. Bookkeeping has been his profession for a long period. I am running and maintaining a blog here: http://www.omeglegirls69.com/
+In [[mathematics]], a [[complex number|complex]] [[Matrix_(mathematics)#Square_matrices|square]] [[matrix (mathematics)|matrix]] ''U'' is '''unitary''' if
+::<math>U^* U = UU^* = I \,</math>
+where ''I'' is the [[identity matrix]] and ''U''* is the [[conjugate transpose]]  of ''U''.
+The real analogue of a unitary matrix is an [[orthonormal]] matrix.
+==Properties==
+For any unitary matrix ''U'', the following hold:
+*Given two complex vectors ''x'' and ''y'', multiplication by ''U'' preserves their [[inner product]]; that is,
+:<math>\langle Ux, Uy \rangle = \langle x, y \rangle</math>.
+*''U'' is [[normal matrix|normal]]
+*''U'' is [[diagonalizable matrix|diagonalizable]]; that is, ''U'' is [[similar matrix|unitarily similar]] to a diagonal matrix, as a consequence of the [[spectral theorem]].  Thus ''U'' has a decomposition of the form
+::<math>U = VDV^*\;</math>
+:where ''V'' is unitary and ''D'' is diagonal and unitary.
+* <math>|\det(U)|=1</math>.
+* Its [[Eigenvector#Eigenspaces_of_a_matrix|eigenspaces]] are orthogonal.
+* For any positive [[integer]] ''n'', the set of all ''n'' by ''n'' unitary matrices with matrix multiplication forms a [[group (mathematics)|group]], called the [[unitary group]] ''U(n)''.
+* Any square matrix with unit Euclidean norm is the average of two unitary matrices.<ref>{{cite journal| first1=Chi-Kwong|last1= Li |first2= Edward|last2= Poon|doi=10.1080/03081080290025507|title=Additive Decomposition of Real Matrices| year=2002| journal=Linear and Multilinear Algebra| volume=50| issue=4| pages=321–326}}</ref>
+==Equivalent conditions==
+If ''U'' is a square, complex matrix, then the following conditions are equivalent:
+#''U'' is unitary
+#''U''*  is unitary
+#''U'' is invertible, with ''U''<sup> –1</sup>=''U''*.
+# the columns of ''U'' form an [[orthonormal basis]] of <math>\mathbb{C}^n</math> with respect to the usual inner product
+# the rows of ''U'' form an orthonormal basis of <math>\mathbb{C}^n</math> with respect to the usual inner product
+# ''U'' is an [[isometry]] with respect to the usual norm
+# ''U'' is a [[normal matrix]] with [[eigenvalues]] lying on the [[unit circle]].
+==See also==
+* [[Orthogonal matrix]]
+* [[Hermitian matrix]]
+* [[Symplectic matrix]]
+* [[Unitary group]]
+* [[Special unitary group]]
+* [[Unitary operator]]
+* [[Matrix decomposition]]
+* [[Identity matrix]]
+* [[Quantum gate]]
+== References ==
+{{reflist}}
+== External links ==
+* {{MathWorld|urlname=UnitaryMatrix |title=Unitary Matrix |last=Rowland|first= Todd}}
+* {{SpringerEOM|id=U/u095540|title=Unitary matrix |first=O. A. |last=Ivanova}}
+{{DEFAULTSORT:Unitary Matrix}}
+[[Category:Matrices]]
+[[Category:Unitary operators]]

Dynamic programming: Difference between revisions

Revision as of 14:38, 15 January 2014

Contents

Properties

Equivalent conditions

See also

References

External links

Navigation menu

Dynamic programming: Difference between revisions

Revision as of 14:38, 15 January 2014

Properties

Equivalent conditions

See also

References

External links

Navigation menu

Search