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Topic: Bilinear operator

Related Topics

Linear transformation

Lie group

Algebra over a field

	Documentation for Concepts 2.0
		The element matrices are computed by the application operator of the bilinear and linear forms (concepts::BilinearForm and concepts::LinearForm).
		A bilinear form is computed in the application operator of a class derived from concepts::BilinearForm.
		The application operator of such an bilinear form takes two elements and an element matrix (which is then filled) as arguments.
	www.math.ethz.ch /~concepts/doxygen/html/group__bilinear.html (413 words)

	Bilinear operator: Definition and Links by Encyclopedian.com
		In general, for a vector space V over a field...over a field F, a bilinear form on V is the same as a bilinear operator V x V -> F.
		In other words, if we hold fixed the first entry to the bilinear operator, while letting the second entry vary, the result is a linear operator, and similarly if we hold fixed the second entry.
		One often thinks of a bilinear operator as a generalized "multiplication" which satisfies the distributive law.
	www.encyclopedian.com /bi/Bilinear-operator.html (487 words)

	Bilinear operator - Wikipedia, the free encyclopedia
		In mathematics, a bilinear operator is a generalized "multiplication" which satisfies the distributive law.
		The set L(V,W;X) of all bilinear maps is a linear subspace of the space (viz vector space, module) of all maps from V×W into X.
		In general, for a vector space V over a field F, a bilinear form on V is the same as a bilinear operator V × V → F.
	en.wikipedia.org /wiki/Bilinear_operator (641 words)

	PlanetMath: bilinear form
		is a symmetric, non-degenerate bilinear form, then the adjoint operation is represented, relative to an orthogonal basis (if one exists), by the matrix transpose.
		See Also: duality with respect to a non-degenerate bilinear form, bilinear map, multi-linear, skew-symmetric bilinear form, symmetric bilinear form, non-degenerate bilinear form
		This is version 47 of bilinear form, born on 2002-01-24, modified 2006-11-06.
	planetmath.org /encyclopedia/BilinearForm.html (294 words)

	Dalí VM Spec
		This operator takes 6 arguments (three planes for the YUV image, and three for the RGB image), and the images that represent the U and V planes are half the width and height of the images that represent the Y, R, G, and B planes.
		The latter operator uses bilinear interpolation to calculate the values of the intermediate pixels.
		Two operations, bit_copy_with_mask and bit_set_with_mask can use a bit image as a mask, to determine which pixels in the output are affected.
	www.cs.cornell.edu /dali/overview.html (3216 words)

	PersonX's Site - Bilinear operator (Site not responding. Last check: 2007-11-02)
		In mathematiсs, a bilinear operator is a generalized "multipliсation" whiсh satisƒies the distributive law.
		is a linear operator ƒrom W to X. In other words, iƒ we hold the ƒirst entry oƒ the bilinear operator ƒixed, while letting the seсond entry vary, the result is a linear operator, and similarly iƒ we hold the seсond entry ƒixed.
		The сase where X is F, and we have a bilinear ƒorm, is partiсularly useƒul (see ƒor example sсalar produсt, inner produсt and գuadratiс ƒorm).
	datind.info /3302 (721 words)

	What's New
		The purpose of this paper is to extend Wolff's sharp bilinear cone restriction estimate to paraboloids, and as a by-product gain some progress on the restriction conjecture for paraboloids and spheres.
		The "bi-Carleson operator" is a sub-bilinear operator which is a natural hybrid between the Bilinear Hilbert transform B(f,g) and the Carleson maximal operator C(f).
		This operator appears naturally in the expansion of Dirac eigenfunctions in one dimension (except for a crucial minus sign, which we discuss in another paper), and is also of similar complexity to the "biest" operator (which is a trilinear operator looking vaguely like B(f,B(g,h)) or B(B(f,g),h), but again not actually factorizable into either form).
	www.math.ucla.edu /~tao/whatsnew2002.html (6040 words)

	PlanetMath: bilinear map
		is said to be a bilinear map if for each
		bilinear function, bilinear operation, bilinear mapping, bilinear operator
		This is version 6 of bilinear map, born on 2005-12-01, modified 2006-03-11.
	planetmath.org /encyclopedia/BilinearOperator.html (103 words)

	Operator algebras
		In analogy to concrete operator spaces we define (cf.
		As in the operator space situation, one can also adopt an abstract point of view: here, this leads to considering Banach algebras which are operator spaces and are equipped with a multiplication compatible with the operator space structure.
		Basic examples of operator algebras are provided by the completely bounded maps on some suitable operator spaces.
	www.math.uni-sb.de /ag/wittstock/OperatorSpace/node48.html (360 words)

	ocean-beach.info Bilinear operator (Site not responding. Last check: 2007-11-02)
		In mathematics ; a bilinear operator is a generalized "multiplication" which satisfies the distributive law.
		In other words; if we hold the first entrу of the bilinear operator fixed; while letting the second entrу varу; the result is a linear operator; and similarlу if we hold the second entrу fixed.
		The case where X is F; and we have a bilinear form ; is particularlу useful (see for example scalar product ; inner product and quadratic form).
	ocean-beach.info /3302 (541 words)

	Bilinear operator - Article from FactBug.org - the fast Wikipedia mirror site
		For a formal definition, given three vector spaces V, W and X over the same base field F, a bilinear operator is a function B : V × W → X such that for any w in W the map
		N, we can define a bilinear operator B : M × N → T, where T is a commutative group, such that for any n in N, m
		The operator B : V × W → X where B(v, w) = 0 for all v in V and w in W is bilinear
	www.factbug.org /cgi-bin/a.cgi?a=4365 (514 words)

	CHAPTER 5 : SECOND ORDER FORMS (Site not responding. Last check: 2007-11-02)
		The fifth term is bilinear in h and k, i.e., it is linear both in h as well as k and is the dominant most mixed expression in h and k.
		Since a bilinear form B(u, v) is a bilinear expression on the cartesian product of a vector space with itself, in this case there arises the possibility of interchanging the areguments in B(u, v) and thus of comparing B(u, v) with B(v, u).
		Prove that: (a) T is singular iff C is singular; (b) the subspaces of symmetric and skew-symmetric bilinear forms are invariant under T; and, (c) T is a projection if C is a projection.
	home.iitk.ac.in /~rksr/html/05form.htm (4654 words)

	Maths -Simultaneous Equations - Martin Baker
		The second definition is an example of a linear map or linear operator.
		A Bilinear function is a function of two variables which is linear when each variable is taken on its own (making the other variables constant).
		This appears so simple that its hardly worth using a special name for it, however, when we are working with quantities made up of several scalars such as vectors then it becomes useful to define the properties of such functions.
	www.euclideanspace.com /maths/algebra/equations/simultaneous/index.htm (762 words)

	Accurate Attenuation Correction in SPECT Imaging using Optimization of Bilinear Functions and Assuming an Unknown ... (Site not responding. Last check: 2007-11-02)
		The proposed algorithm is based on the iterative methods for solving linear operator equations.
		Whenever an operator F is the sum of a linear and a bilinear operator, a modi ed iteration sequence can be de ned.
		In, a bilinear approximation R to R was introduced: R(f; Z R f(s t)e R 1 t 0 (s)d (1 Z 1 t (s)d)...
	citeseer.ist.psu.edu /398308.html (705 words)

	cccr.info Bilinear operator (Site not responding. Last check: 2007-11-02)
		In mathematicѕ ; a bilinear operator iѕ a ցeneralized "multiplication" which ѕatiѕfieѕ the diѕtributive law ·
		For a formal definition; ցiven three vector ѕpace ѕ V; W and X over the ѕame baѕe field (mathematicѕ) F; a bilinear operator iѕ a function (mathematicѕ) :B : V &timeѕ; W → X ѕuch that for any w in W the map :
		N; we can define a bilinear operator B : M &timeѕ; N → T; where T iѕ a commutative ցroup (mathematicѕ) ; ѕuch that for any n in N; m
	cccr.info /3302 (609 words)

	Algebra over a field - Wikipedia, the free encyclopedia
		Let K be a field, and let A be a vector space over K equipped with a binary operation (ie if x and y are any two elements ("vectors")of A, xy is the product of x and y).
		Then if the binary operation is bilinear, which means that the following identities hold for any three elements x, y, and z of A, and all elements ("scalars") a and b of K:
		For algebras over a field, the bilinear multiplication from A × A to A is completely determined by the multiplication of basis elements of A.
	en.wikipedia.org /wiki/Algebra_over_a_field (1323 words)

	The full two-grid operator (Site not responding. Last check: 2007-11-02)
		denote the two-grid operator and the full two-grid operator, respectively.
		Therefore the error transition operator of the full two-grid operator can be expressed as
		Remark 3 For the multigrid method discussed here bilinear interpolation and the transposed restriction is assumed.
	hej.sze.hu /ANM/ANM-980724-A/anm980724a/node6.html (218 words)

	Poisson Brackets
		Dirac, in "The Principles of Quantum Mechanics", begins the fourth Chapter, "The Quantum Conditions", with a section on an operator called the Poisson Bracket.
		So while a general bilinear operator, such as τ builds, can involve a permutation, the multiplication we want to be using is one which doesn't alter the order of the pieces multiplied.
		Crucially, given that we'll be involving differential operators, all the τ operators are mapped to zero by any Leibniz operator, including any differential operator; that is, the τ operators are constant.
	www.chaos.org.uk /~eddy/physics/poisson.html (1460 words)

	Documentation for Concepts 2.0
		operator() (const uint i, const uint j) const =0
		This assembly operator uses the element pairs taken from
		This assembly operator does not compute element matrices for two different elements.
	www.math.ethz.ch /~concepts/doxygen/html/classconcepts_1_1Matrix.html (395 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		The MACSYMA programs are tested by constructing exact solutions of various nonlinear partial differential equations from soliton theory, such as the Korteweg-de Vries, the Sawada-Kotera, the modified Korteweg-de Vries, the Kadomtsev-Petviashvili, the Boussinesq equation, the shallow water wave equations and many others.
		The development of a computer program that calculates soliton solutions of an entire family of coupled bilinear systems is under development.
		To run the KdV case at the prompt (c1) under Macsyma on your PC, type batch("c:\\macsyma\\hirota\\h_kdv.com"); ------- The programs require little interaction from the user, who must provide the bilinear operator(s) for the original PDE and specify which soliton solution (one, two or three) should be calculated.
	www.mines.edu /fs_home/whereman/software/hirota/h_readme.txt (1168 words)

	Irrlicht Engine: irr::video::SMaterial Struct Reference (Site not responding. Last check: 2007-11-02)
		In Irrlicht you can use anisotropic texture filtering in conjunction with bilinear or trilinear texture filtering to improve rendering results.
		If the trilinear filter flag is enabled, the bilinear filtering flag is ignored.
		May be written to the zbuffer or is it readonly.
	irrlicht.sourceforge.net /docu/structirr_1_1video_1_1_s_material.html (458 words)

	DIMEFEM: High-level Portable Irregular-Mesh Finite-Element Solver (Site not responding. Last check: 2007-11-02)
		The data objects dealt with by DIMEFEM are finite-element functions (FEFs), which may be scalar or have several components (vector fields), as well as linear, multilinear and nonlinear operators which map these FEFs to numbers.
		The guiding principle is that interesting physical problems may be expressed in variational terms involving FEFs and operators on them [Bristeau:87a], [Glowinski:84a].
		We now define the linear operator L and bilinear operator a as above, and call the linear solver to evaluate u.
	www.netlib.org /utk/lsi/pcwLSI/text/node241.html (177 words)

	A Uniform Estimate for the Quartile Operator (ResearchIndex) (Site not responding. Last check: 2007-11-02)
		There is a one parameter family of bilinear Hilbert transforms.
		L 1;1 uniformly for a discrete family of model operators for the bilinear Hilbert transform.
		Introduction The quartile operator, introduced in [8],[9], is a discrete model for the bilinear Hilbert...
	citeseer.ist.psu.edu /298825.html (232 words)

	Vector space - Wikipedia, the free encyclopedia
		Vector spaces are the basic objects of study in linear algebra, and are used throughout mathematics, science, and engineering.
		A vector space with a topology compatible with the operations — such that addition and scalar multiplication are continuous maps — is called a topological vector space.
		A vector space with a bilinear operator (defining a multiplication of vectors) is an algebra over a field.
	en.wikipedia.org /wiki/Vector_space (1577 words)

	Table of Contents
		HCL_DiagScaleLinearOp_d HCL_DiagScaleLinearOp_d is a class implementing the linear operator mapping x to ax, where x and a are vectors and the multiplication is done componentwise (in "Matlab notation", this operation* is a
		HCL_OpDefaultDeriv_d HCL_OpDefaultDeriv_d is a linear operator class implementing the derivative of a nonlinear operator
		HCL_OpDefaultSecondDeriv_d HCL_OpDefaultSecondDeriv_d is a bilinear operator class implementing the second derivative of a nonlinear operator
	www.trip.caam.rice.edu /txt/hcldoc/html/aindex.html (2273 words)

	Mathematics of Sampled Data Systems
		Starting in the Laplace domain, the Laplace operator ‘s’ is replaced by a first order difference operator, i.e.
		The index indicates how many integer multiples of the sampling interval is involved in the time shift, with the sign of the index denoting whether it is a forward (plus sign) or backward (minus sign) shift.
		The Bilinear Transform is also known as Tustin's Rule as well as the more familiar Trapezoidal Rule used in numerical integration.
	lorien.ncl.ac.uk /ming/digicont/digimath/sampled2.htm (333 words)

	What's New
		Here we consider multilinear operators similar to that of the bilinear Hilbert transform, but with an additional polynomial phase oscillation (thus these are the multilinear analogue of the singular oscillatory integrals studied for instance by Ricci and Stein, and are also related to the polyomial phase Carleson maximal operators studied for instance by Lacey).
		It turns out that one can fairly quickly decouple the singular and oscillatory parts of this operator into a singular piece where the oscillation is not significant (and which can be dealt with by existing multilinear multiplier theorems), plus an oscillatory part where the singularity of the kernel is irrelevant.
		Indeed, we also show in the paper that if we consider the simplest biparameter operator of bilinear Hilbert transform type, namely the double bilinear Hilbert transform, then this operator is in fact unbounded in any Lebesgue space (this may have been discovered earlier as “folklore”, but does not appear explicitly in print).
	www.math.ucla.edu /~tao/whatsnew2003.html (3928 words)

	FreeFEM3D (aka ff3d): VariationalProblem Class Reference
		Adds a variational "border" bilinear operator to its list
		Adds a variational bilinear operator to its list
		list of bilinear border operators, ie operators living on the border for natural BC as an example
	www.freefem.org /ff3d/doxygen/classVariationalProblem.html (267 words)

	symplectic
		This is a 2-dimensional complex vector space H equipped with angular momentum operators satisfying the usual commutation relations:
		But an antiunitary operator with these properties does exist, and is unique up to phase.
		And of course this is completely general: if we have two unitary group representations, any conjugate-linear intertwining operator from one to the other will commute with the group action and thus commute with the skew-adjoint generators, but it will anticommute with the self-adjoint generators that physicists prefer to work with.
	math.ucr.edu /home/baez/symplectic.html (2392 words)

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