
	Where results make sense

Topic: Direct sum

Related Topics

Direct product

Wedge product

Square matrix

Abelian group

Glossary of ring theory

Quartic equation

Galois theory

Cubic equation

Sulfur bridges

Stone tool

Trypsin

Lalaine Miranda

Chester Bowles

Niels Henrik Abel

Xu Chu

In the News (Sun 22 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Direct sum of modules - Wikipedia, the free encyclopedia
		The dimension of V ⊕ W is equal to the sum of the dimensions of V and W.
		In the language of category theory, the direct sum is a coproduct and hence a colimit in the category of left R-modules, which means that it is characterized by the following universal property.
		The direct sum of two Banach spaces X and Y is the direct sum of X and Y considered as vector spaces, with the norm (x,y)
	en.wikipedia.org /wiki/Direct_sum (1497 words)

	Direct sum of groups - Wikipedia, the free encyclopedia
		In abstract algebra, this method of construction can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum for more information.
		This notation is commutative; so that in the case of the direct sum of two subgroups, G = H + K = K + H.
		Thus, in a sense, the direct sum is an "internal" external direct sum.
	en.wikipedia.org /wiki/Direct_sum_of_groups (654 words)

	Direct sum (Site not responding. Last check: 2007-10-21)
		In abstract algebra, the direct sum is a construction which combines several vector space s (or groups, or abelian group s, or modules) into a new, bigger one.
		The direct sum of two Banach space s X and Y is the direct sum of X and Y considered as vector spaces, with the norm (x'',''y)
		Direct Access Democracy Proposes a form of direct democracy in which voting is done in small groups, the results of which are binding upon elected representatives.
	www.serebella.com /encyclopedia/article-Direct_sum.html (1573 words)

	Direct article - Direct route Direct access database Direct connect telecommunications - What-Means.com (Site not responding. Last check: 2007-10-21)
		A direct route or service is the one that goes between the start and end points without diverting to a third location en route.
		In abstract algebra, the direct sum is a construction which combines several vector spaces.
		Mars Direct is a proposal for a relatively low-cost manned mission to Mars.
	www.what-means.com /encyclopedia/Direct (200 words)

	SUM - Definition
		The principal points or thoughts when viewed together; the amount; the substance; compendium; as, this is the sum of all the evidence in the case; this is the sum and substance of his objections.
		A sum in arithmetic wherein a flaw discovered at a particular point is ipso facto fatal to the whole.
		{Algebraic sum}, as distinguished from arithmetical sum, the aggregate of two or more numbers or quantities taken with regard to their signs, as + or -, according to the rules of addition in algebra; thus, the algebraic sum of -2, 8, and -1 is 5.
	www.hyperdictionary.com /dictionary/sum (691 words)

	Direct sum (Site not responding. Last check: 2007-10-21)
		Direct sums are also commutative and meaning that it doesn't matter in which one forms the direct sum.
		The direct sum of two Banach spaces X and Y is the direct sum of X and Y considered as vector spaces with the (x y)
		The norm is given by the sum The direct sum with this norm is a Banach space.
	www.freeglossary.com /Direct_sum (1569 words)

	Direct sum of groups -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Loosely speaking, a direct sum is isomorphic to a (Click link for more info and facts about direct product) direct product of subgroups.
		This notation is (Click link for more info and facts about commutative) commutative; so that in the case of the direct sum of two subgroups, G = H + K = K + H.
		The direct sum is not unique for a group; for example, in the (Click link for more info and facts about Klein group) Klein group, V
	www.absoluteastronomy.com /encyclopedia/d/di/direct_sum_of_groups.htm (711 words)

	Digital Sum (Site not responding. Last check: 2007-10-21)
		The digital sum in base b of a set of natural numbers is calculated as follows: express each of the numbers in base b, then take the sum of corresponding digits and discard all carry overs.
		The digital sum in base b is an associative and commutative operation on the natural numbers; it has 0 as neutral element and every natural number has an inverse element under this operation.
		The natural numbers together with the base-b digital sum thus form an abelian group; this group is isomorphic to the direct sum of a countable number of copies of Z/bZ.
	www.wikiverse.org /digital-sum (362 words)

	NMR
		The basic deal with the Ewald method is that the conditionally convergent Coulombic sum is transformed into a sum of two rapidly converging sums: the direct sum (a sum in real space) and a reciprocal sum (a sum in reciprocal space).
		This way, we only need to calculate the terms of the direct sum over our interacting pairs (the pairlist) and can calculate the direct sum at the same time we are doing the standard lennard jones terms.
		direct sum is extremely short ranged) then make sure the direct sum value at the cutoff is less than the tolerance.
	amber.scripps.edu /Questions/ewald.html (2323 words)

	Characterizations of semisimple modules (Site not responding. Last check: 2007-10-21)
		E is the direct sum of a family of simple submodules.
		Every submodule F of E is a ``direct summand'', that is, has a ``complementary'' submodule F' in E such that E is the direct sum of F and F'.
		Then S' is simple, since the direct sum of any submodule with M is a submodule of Rv containing M and thus equal to either M (when the submodule is {0}) or Rv (when it is all of S').
	www.math.harvard.edu /~elkies/M250.04/semisimple.html (569 words)

	PlanetMath: direct sum of even/odd functions (example)
		"direct sum of even/odd functions (example)" is owned by mathcam.
		Cross-references: equation, sum, components, vector subspaces, mapping, zero vector, operations, constant, real, structure, vector space, even functions, functions, contain, odd functions, direct sum
		This is version 3 of direct sum of even/odd functions (example), born on 2003-04-16, modified 2004-03-23.
	planetmath.org /encyclopedia/DirectSumOfEvenoddFunctionsExample.html (114 words)

	PlanetMath: direct sum
		The direct sum is often referred to as the weak direct sum or simply the sum.
		Often an internal direct sum is written as
		This is version 6 of direct sum, born on 2002-01-05, modified 2005-04-24.
	planetmath.org /encyclopedia/DirectSum.html (110 words)

	Directory of open access journals
		We show that a direct sum operator does not depend in a straightforward manner on the separate operators involved.
		That is, on having a set of self-adjoint operators giving a direct sum operator, we show how the spectral representation for this operator depends on the spectral representations for the individual operators (the coordinate operators) involved in forming this sum operator.
		In particular it is shown that this problem is not immediately solved by taking a direct sum of the spectral properties of the coordinate operators.
	www.doaj.org /abstract?id=89054&toc=y (215 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Confluence is not preserved across direct sum of a finite num ber of systems, even when these are non-collapsing.
		Confluence is preserved under the direct sum of a finite number of non-collapsing systems if only terms of finite rank are considered.
		Top-termination is preserved under the direct sum of a finite number of left-linear systems.
	www.diku.dk /~simonsen/abstracts/pj4.html (198 words)

	Online Dictionary for French English, Spanish English, Italian English, and more.
		Immediate or direct in bearing or force; having nothing intervening; "in direct sunlight"; "in direct contact with the voters"; "the direct cause of the accident." 4.
		Extended senses; direct in means or manner or behavior or language or action; "a direct question"; "a direct response"; "a direct approach." 7.
		A union of two disjoint sets in which every element is the sum of an element from each of the disjoint sets.
	www.ultralingua.net /?service=ee&text=direct (595 words)

	Direct: Rising Sum (Site not responding. Last check: 2007-10-21)
		Direct recently spoke with Saul Gitlin, executive vice president of strategic marketing services/new business for New York-based agency Kang & Lee, on the potential of this market.
		Gitlin received a bachelor's degree in Asian studies with a focus on Chinese at Cornell, and in 1982 was one of the first three Cornell undergraduates to spend a year as an exchange student in the People's Republic of China.
		The point of entry for most of these marketers has been to build a presence in the Asian mass media, which is very high profile in some areas of the country and very cost-efficient, because of the lost cost of insertion in print and broadcast.
	www.findarticles.com /p/articles/mi_m3815/is_9_15/ai_103878567 (1085 words)

	Direct Sum 2
		is a direct sum of the subspaces and denote
		Example Since the only symmetric and skew symmetric matrix is the zero matrix, the sum of the subspace of symmetric matrices and the subspace of skew-symmetric matrices is a direct one.
		matrices is the direct sum of symmetric and skew symmetric matrices.
	algebra.math.ust.hk /vector_space/13_direct_sum/lecture2.shtml (242 words)

	Direct Sum of Vector Spaces (Site not responding. Last check: 2007-10-21)
		If u and v are disjoint (except for 0), then the span is called the sum, or the direct sum, or the direct product.
		In summary, the span is a direct sum (i.e.
		Subspaces are complementary if they are invariant and their direct sum produces the original space.
	www.mathreference.com /la-jf,sum.html (487 words)

	A.D. Bell: Abstract (Site not responding. Last check: 2007-10-21)
		In this paper we study the ideal structure of the direct limit and direct sum (with a special multiplication) of a directed system of rings; this enables us to give descriptions of the prime ideals and radicals of semigroup rings and semigroup-graded rings.
		We show that the ideals in the direct limit correspond to certain families of ideals from the original rings, with prime ideals corresponding to ``prime'' families.
		We then assume the indexing set is a semigroup $\Omega$ with preorder defined by $\alpha\lt\beta$ if $\beta$ is in the ideal generated by $\alpha$, and we use the direct sum to construct an $\Omega$\!-graded ring; this construction generalizes the concept of a strong supplementary semilattice sum of rings.
	www.uwm.edu /~adbell/Research/Abstracts/systemsums.html (222 words)

	Multiplication of Sets
		Both have counterparts (set union and direct sum, respectively) sheer existence of which makes the terminology quite arbitrary.
		We met direct sums when talking of Boolean Algebras.
		Now, the definition is actually confusing because as often as not the same set of pairs is called the direct product of the two sets A and B. Some distinction is drawn when we consider direct sums and products of an infinite numbers of sets.
	www.cut-the-knot.com /do_you_know/mul_set.shtml (415 words)

	Direct Sum (Module) (Site not responding. Last check: 2007-10-21)
		The direct sum of an arbitrary family of
		Modules, then the direct sum is represented by the collection of functions with finite support from
		The significant property of the direct sum is that it is the coproduct in the category of
	www.math.sdu.edu.cn /mathency/math/d/d252.htm (79 words)

	DC MetaData for: Dequantisation: Direct and Semi-Direct Sums of Idempotent Semimodules (Site not responding. Last check: 2007-10-21)
		DC MetaData for: Dequantisation: Direct and Semi-Direct Sums of Idempotent Semimodules
		We give here a necessary and sufficient condition for an idempotent semimodule to be the direct sum of two subsemimodules.
		We introduce the semi-direct sum of semilattices, extend it to idempotent semimodules, and then use the concepts of torsion, Boolean, and semi-Boolean semimodules, to show how a general semimodule over an idempotent semiring splits into a semi-direct sum of a free, a Booelan, a semi-Boolean and a torsion semimodule.
	www.esi.ac.at /Preprint-shadows/esi1442.html (221 words)

	Direct Sum/Product and PID Quotients
		Write a as the direct sum of quotients of free modules, and expand each module in the aforementioned exact sequence into its direct sum.
		The homology is the direct sum of the component homologies, and tor commutes with direct sum.
		Since dual and direct sum do not commute, we can't make any claims about ext(a,b) when a or b is an infinite direct sum.
	www.mathreference.com /mod-hom-te,sumpid.html (474 words)

	Matrix addition : Direct sum (Matrix) (Site not responding. Last check: 2007-10-21)
		The sum of two m-by-n matrices A and B, denoted by A + B, is again an m-by-n matrix computed by adding corresponding elements, i.e., (A + B)[i, j] = A[i, j] + B[i, j].
		For any arbitrary matrices A (of size m × n) and B (of size p × q), we have the direct sum of A and B, denoted by AB and defined as
		It uses material from the wikipedia article Matrix addition : Direct sum (Matrix).
	www.eurofreehost.com /di/Direct_sum_(Matrix).html (302 words)

	Citations: Vector Quantizers with Direct Sum Codebooks - Barnes, Frost (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		However, the complexity of such an encoder exceeds that of an exhaustive search of the direct sum codebooks.
		This method is a heuristic compromise between component wise optimization and exhaustive search where the association is done in multiple stages bringing the codebook closer to the data point at each stage.
		Next the error of this first stage is quantized into the closer of Gammaff 1 and ff 1, and so on until an approximation to x of the form in (27) is....
	citeseer.ist.psu.edu /context/158207/0 (1405 words)

	Maybe this Explains the Economic Cycle... best Complete Direct Sum (Site not responding. Last check: 2007-10-21)
		direct sum - a union of two disjoint sets in which every element is the sum of...
		The direct sum of injective modules need not be...
		We then define the direct sum of the Hilbert spaces Hi to be...
	ascot.pl /th/Fourier3/Complete-Direct-Sum.htm (630 words)

	Nathan Urban, John Baez: Tensor Product and Direct Sum
		Isn't the direct sum of two vector spaces V and V' just the space of all pairs (v,v') where v is in V and v' is in V'?
		Yes, the direct sum of two Hilbert spaces is just their Cartesian product, made into a Hilbert space in a fairly obvious way.
		It may seem weird that the direct sum of vector spaces is both the product and coproduct, but it's true: this is part of Vect being an "abelian category".
	www.math.ucr.edu /home/baez/photon/tensor.htm (793 words)

	Multiplicative Complexity Of Direct Sum Of Quadratic Systems (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		We study classes of direct sums of quadratic forms.
		For these classes of problems we show that the complexity of one direct sum is the sum of the complexities of the summands and that every minimal quadratic algorithm for computing the direct sums is a direct-sum algorithm.
		2 the validity of the direct sum conjecture (context) - Ja'Ja', Takche - 1986
	citeseer.ist.psu.edu /132742.html (690 words)

Try your search on: Qwika (all wikis)