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Topic: Normed vector space

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Norm (mathematics)

Vector space

Dual space

Seminorm

Operator norm

Vector space

Banach space

Vector space example 1

Inner product space

Hahn Banach theorem

	PlanetMath: normed vector space
		It follows that any normed space is a locally convex topological vector space, in the topology induced by the metric defined above.
		norm, metric induced by a norm, metric induced by the norm, induced norm
		This is version 10 of normed vector space, born on 2002-01-24, modified 2006-12-08.
	planetmath.org /encyclopedia/NormedVectorSpace.html (249 words)

	NationMaster - Encyclopedia: Normed vector space (Site not responding. Last check: 2007-10-11)
		A semi normed vector space is a pair (V,p) where V is a vector space and p a semi norm on V.
		This turns the semi normed space into a semi metric space (notice this is weaker than a metric) and allows the definition of notions such as continuity and convergence.
		The definition of many normed spaces (in particular, Banach spaces) involves a seminorm defined on a vector space and then the normed space is defined as the quotient space by the subspace of elements of seminorm zero.
	www.nationmaster.com /encyclopedia/Normed-vector-space (2540 words)

	Normed vector space
		4 Normed spaces as quotient spaces of semi normed spaces
		A semi normed vector space is a 2-tuple (V,p) where V is a vector space and p a semi norm on V.
		Normed spaces as quotient spaces of semi normed spaces
	www.brainyencyclopedia.com /encyclopedia/n/no/normed_vector_space.html (960 words)

	Kids.Net.Au - Encyclopedia > Normed vector space (Site not responding. Last check: 2007-10-11)
		is a romboid[?], for the 2-norm (Euclidian norm) it is the well-known unit circle, while for the infinity norm it is a square.
		All norms on a finite-dimensional vector space V are equivalent.
		A surjective isometry between the normed vector spaces V and W is called a isometric isomorphism, and V and W are called isometrically isomorphic.
	www.kids.net.au /encyclopedia-wiki/no/Normed_vector_space (850 words)

	PlanetMath: every finite dimensional normed vector space is a Banach space
		Since all norms on a finite dimensional vector space are equivalent, there is a constant
		"every finite dimensional normed vector space is a Banach space" is owned by matte.
		This is version 7 of every finite dimensional normed vector space is a Banach space, born on 2005-01-09, modified 2005-02-18.
	planetmath.org /encyclopedia/EveryFiniteDimensionalNormedVectorSpaceIsABanachSpace.html (127 words)

	PlanetMath: normed vector space
		The norm is a convex function of its argument.
		norm, metric induced by a norm, metric induced by the norm, induced norm
		This is version 10 of normed vector space, born on 2002-01-24, modified 2006-12-08.
	www.planetmath.org /encyclopedia/NormedVectorSpace.html (249 words)

	Normed vector space - ExampleProblems.com (Site not responding. Last check: 2007-10-11)
		A semi normed vector space is a pair (V,p) where V is a vector space and p a semi norm on V.
		This turns the semi normed space into a semi metric space (notice this is weaker than a metric) and allows the definition of notions such as continuity and convergence.
		All norms on a finite-dimensional vector space are equivalent from a topological point as they induce the same topology (although the resulting metric spaces need not be the same).
	www.exampleproblems.com /wiki/index.php/Normed_linear_space (1005 words)

	Normed vector space - Definition, explanation
		A semi normed vector space is a 2-tuple (V,p) where V is a vector space and p a semi norm on V.
		A normed vector space is a 2-tuple (V,·) where V is a vector space and ·
		Normed spaces as quotient spaces of semi normed spaces
	www.calsky.com /lexikon/en/txt/n/no/normed_vector_space.php (889 words)

	Normed Vector Space
		A normed vector space, also called a normed linear space, is a real vector space S with a norm function denoted x.
		Thus d becomes a distance metric, and S is a metric space, with the open ball topology.
		A banach space is a normed vector space that forms a complete metric space.
	www.mathreference.com /top-ban,nvs.html (749 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: 2007-10-11)
		Vector spaces are the basic objects of study in linear algebra, and are used throughout mathematics, science, and engineering.
		Vectors in these spaces are ordered pairs or triples of real numbers, and are often represented as geometric vectors which are quantities with a magnitude and a direction, usually depicted as arrows.
		Given a vector space V, a nonempty subset W of V that is closed under addition and scalar multiplication is called a subspace of V. Subspaces of V are vector spaces (over the same field) in their own right.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=vector_space (1581 words)

	NationMaster - Encyclopedia: Hahn Banach theorem (Site not responding. Last check: 2007-10-11)
		It allows one to extend linear operators defined on a subspace of some vector space to the whole space, and it also shows that there are "enough" continuous linear functionals defined on every normed vector space to make the study of the dual space interesting.
		If V is a vector space over the scalar field K (which is either the real numbers R or the complex numbers C), we call a function N : V → R sublinear if
		If V is a normed vector space with subspace U (not necessarily closed) and if z is an element of V not in the closure of U, then there exists a continuous linear map ψ ;: V → K with ψ(x) = 0 for all x in U, ψ(z) = 1, and ψ
	www.nationmaster.com /encyclopedia/Hahn_Banach-theorem (530 words)

	Vector space Summary
		A vector is formally, an element of a vector space.
		In this case, the scalar (1/2) was multiplied by the vector (60 mph west) and the result is the vector (30 mph west).
		Vectors in these spaces are ordered pairs or triples of real numbers, and are often represented as geometric vectors (quantities with a magnitude and a direction, usually depicted as arrows).
	www.bookrags.com /Vector_space (4366 words)

	More on Vector Spaces
		Given a vector space V, any nonempty subset W of V which is closed under addition and scalar multiplication is called a subspace of V. It is easy to see that subspaces of V are vector spaces (over the same field) in their own right.
		Given two vector spaces V and W over the same field F, one can define linear transformations or “linear maps” from V to W. These are maps from V to W which are compatible with the relevant structure—i.e., they preserve sums and scalar products.
		The definition of a vector space makes perfectly good sense if one replaces the field of scalars F by a general ring R. The resulting structure is called a modules over R. In other words, a vector space is nothing but a module over a field.
	www.artilifes.com /vector-spaces.htm (1272 words)

	Orðasafn: N
		norm topology staðalgrannmynstur, -> metric topology, -> strong topology.
		normed linear space staðlað línulegt rúm, staðlað vigurrúm, staðlað vektorrúm, = normed space, = normed vector space.
		null vector 1 núllvigur, núllvektor, = zero vector.
	www.hi.is /~mmh/ord/safn/safnN.html (1139 words)

	MC243 Aspects of Linear Analysis
		A second application of the theory of Hilbert spaces is in the study of orthogonal complements; this extends the idea of the Cartesian coordinate system, whereby we use two perpendicular axes in order to describe every point in the plane.
		Normed vector space, examples, continuous mapping between normed vector spaces, the continuity properties of a norm.
		,norm of a composition of bounded linear operators, concept of equivalent norms, to know that all norms on a finite-dimensional vector space are equivalent, example of inequivalent norms.
	www.mcs.le.ac.uk /Modules/Year4/MC243.html (667 words)

	FuncAna
		Dual space of normed vector space is a Banach space.
		Local weak compactness of the dual spaces of normed vector spaces: closed bounded sets in the dual space are weakly compact.
		Norm of a self-adjoint operator is equal to the supremum of the absolute value of its quadratic form on the unit sphere.
	www.math.ttu.edu /~vshubov/FuncAna/FuncAna.html (947 words)

	Most Recent Proofs - Metamath Proof Explorer
		The predicate "is a complex Hilbert space." A Hilbert space is a Banach space which is also an inner product space, i.e.
		A complex Banach space is a normed complex vector space with a complete induced metric.
		The norm of a normed complex vector space is a real number.
	us2.metamath.org:8888 /mpegif/mmrecent.html (4735 words)

	long distance phone cards (Site not responding. Last check: 2007-10-11)
		Calculating a position with the Lp space, the function of a rigid body does not define a metric, long distance puone card canada but gives a premetric (or metric space) on the translation (geometry) of the approaching aircraft from the context what (semi) norm we are using.
		For any semi normed vector space and middot; a norm (mathematics) on V. A normed vector has a positive length.
		Multiplying a vector space V is finitedimensional if and only if the pilot can zero out the angle increases.
	long-distance-phone-cards.seekmsn.info (941 words)

	John Synowiec
		Introduction to Partial Differential Equations and Hilbert Space
		Methods, by K. GUSTAFSON in SIAM Review 25 (1983) pp 110 - 111.
		Review of: Introduction to Hilbert Spaces With Applications, by L. DEBNATH and
	www.iun.edu /~mathjas (510 words)

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