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	Normed vector space - Wikipedia, the free encyclopedia
		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 surjective isometry between the normed vector spaces V and W is called a isometric isomorphism, and V and W are called isometrically isomorphic.
		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.
	en.wikipedia.org /wiki/Normed_vector_space (889 words)

	Linear algebra - FreeEncyclopedia (Site not responding. Last check: 2007-10-09)
		Linear Algebra the branch of mathematics concerned with the study of vectors, vector spaces, linear transformations, and systems of linear equations.
		A vector space (or linear space), as a purely abstract concept about which we prove theorems, is part of abstract algebra, and well integrated into this field.
		Linear operators take elements from a linear space to another (or to itself), in a manner that is compatible with the addition and scalar multiplication given on the vector space(s).
	openproxy.ath.cx /li/Linear_algebra.html (654 words)

	Vector space (Site not responding. Last check: 2007-10-09)
		The fundamental concept in linear algebra is that of a vector space or linear space.
		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.
	www.sciencedaily.com /encyclopedia/vector_space_1 (1117 words)

	Abstract linear spaces
		This is an important step in the axiomatisation of geometry and an early move towards the necessary abstraction for the concept of a linear space to arise.
		The parallel development in analysis was to move from spaces of concrete objects such as sequence spaces towards abstract linear spaces.
		Peano defines linear operators on a linear space, shows that by using coordinates one obtains a matrix.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Abstract_linear_spaces.html (1865 words)

	Linear Vector Spaces (Site not responding. Last check: 2007-10-09)
		The space of ordinary vectors in three-dimensional space is 3-dimensional.
		is a subspace of the space of ordinary vectors in 3 dimensions.
		The vector space that all possible states belong to in QM is not 3-dimensional, but infinite-dimensional.
	electron6.phys.utk.edu /qm1/modules/m3/Vector_space.htm (1211 words)

	Linear Combination of Vectors, and the Linear Vector Space.
		Linear Combination of Vectors, and the Linear Vector Space.
		space is thus a three dimensional linear vector room, where we let each point correspond to a position vector.
		If a set of vectors is a base for a linear space, then the set of coordinates for a point x are unique.
	www.torget.se /users/m/mauritz/math/vect/linear.htm (406 words)

	The Geometric Algebra of 3D Euclidean Space
		The axioms for a vector space are designed to encode the intuitive idea of addition of arrows and multiplication of an arrow by a number.
		Again the space is oriented so that there is a sense of unrolling and rolling space that corresponds to positive and negative volumes.
		The objects in the geometric algebra are particularly useful for representing the isometries of the space.
	omega.albany.edu:8008 /mat220dir/ga3d-dir/GA3d.html (2218 words)

	System and method for image mapping in linear space - Patent 5598186
		In contrast, if a linear lumen scale is selected, 42, capable of resolving original nonlinear input as, for example, in shadows, then the linear representation must have 224 states shown at reference numeral 41 to match just 16 states of input shown at reference numeral 40.
		The linear image is precalculated so that error-correcting addition or subtraction is made prior to the pixel's conversion or, to save memory space, the value to add or subtract is stored in an array so that it may be added when the pixel is converted.
		The linear image 90 may be precalculated so that this addition and subtraction can be made ahead of the pixel thereafter being converted, or, to save memory space, the value to add and subtract may be kept in an array so that it may be added when the pixel is converted.
	freepatentsonline.com /5598186.html (4472 words)

	Utilizing Straight Lines in Object Space for Linear Array (Site not responding. Last check: 2007-10-09)
		Linear array scanners have one or more 1-D arrays of CCD sensors in the image plane.
		The underlying principal is that the vector from the perspective center to a scene point on a straight-line feature lies on the plane defined by the perspective center and the two object points defining the straight line.
		For linear array scanner imagery, the straight-line feature is not straight in image space, and is evaluated at all image points along the line.
	www.people.cornell.edu /pages/aa243/research/linear.html (754 words)

	CS554A Syllabus: Memory Management Tutorial. (Site not responding. Last check: 2007-10-09)
		The linear address is then checked against the segment size to protect the system against accesses outside the segment: if the computed linear address falls outside the segment, a segment protection fault is typically generated.
		The application space is therefore treated as a virtual addressing space, not necessarily contiguously implemented in the actual machine's physical memory.
		Some of that space may be unmapped, and some may have had their physical pages swapped out to mass storage.
	www.rivier.edu /faculty/amoreira/web/cs554a/Tut3 (1676 words)

	linear space : Definition from the Online Dictionary at Datasegment.com (Site not responding. Last check: 2007-10-09)
		1 definition found linear space - Free On-line Dictionary of Computing (19 Sep 2003) : linear space A vector space where all linear combinations of elements are also elements of the space.
		This is easy for spaces of numbers but not for a space of functions.
		Roughly, this is to say that multiplication by numbers, and addition of elements is defined in the space.
	onlinedictionary.datasegment.com /word/linear+space (75 words)

	AIM: The Linear Intensity Space
		Often the input device linearization is not needed since high-end digital cameras and scanners are linear already.
		Fully saturated pixels cover the whole pixel area but even then pixels do not have even intensity over their are, the center of the pixel area is more saturated than the edges, see some images about it.
		Gamma curves can be used for linearizing an image that has a known file-gamma (in case images were created on an un-calibrated system the correct curve is gamma 2.5).
	www.aim-dtp.net /aim/calibration/linear_intensity_space/linear.htm (1963 words)

	Monocosm: a linear solution to the effective four-dimensionality problem, a topos-theoretic look at the foundations of ...
		Example: in quantum theory the observer’s actions are represented by operators on a linear space and constitute, together with an associative composition, a semi-group with an identity (monoid).
		The linear case of this structure is, of course, a real linear associative algebra A with an identity.
		is the tangent space of expA at the identity.
	home.netcom.com /~trifonov (2849 words)

	Linear Spaces (Site not responding. Last check: 2007-10-09)
		If S is also a linear space over K with the same operation of addition and multiplication by scalars, then S is called a subspace.
		Let V be the linear space of all functions from an interval [a,b] into the real field.
		The set of all finite linear combinations of elements in S, denoted by L(S), is a subspace of V.
	mwt.e-technik.uni-ulm.de /world/lehre/basic_mathematics/di/node22.php3 (506 words)

	Vector Space Concepts
		A linear space is sometimes be called a linear vector space, or a vector space.
		A normed linear space is a linear space
		A Banach Space is a complete normed linear space, that is, a normed linear space in which every Cauchy sequence
	ccrma-www.stanford.edu /~jos/gradient/Vector_Space_Concepts.html (252 words)

	A brief survey of linear algebra (Site not responding. Last check: 2007-10-09)
		Beyond that, linear algebra courses are often the transition from lower division mathematics courses such as calculus, probability/statistics, and elementary differential equations, which typically focus on specific problem solving techniques, to the more theoretical axiomatic and proof oriented upper division mathematics courses.
		In linear algebra, we have the nice property that if a linear transformation is bijective, then its inverse is also linear, and thus it is an isomorphism.
		Thus, two isomorphic vector spaces are indistinguishable as vector spaces except for a renaming of the elements.
	astarte.csustan.edu /~tom/SFI-CSSS/linear-algebra/lin-alg.html (4998 words)

	AIM: Photoshop Color Settings
		It is important to note that in order to actually work with linear image data the non-linear images must be converted to the linear working-space (the middle choice in the Embedded Profile Mismatch -dialog).
		If the "Use the embedded profile (instead of the working space)" -option is chosen when images are opened then the image data remains non-linear and Photoshop only performs the required compensation on-the-fly for the monitor only.
		A color space (also known as color gamut) defines the saturation range that the particular gamut holds, most saturated colors are at the gamut edge.
	www.aim-dtp.net /aim/photoshop/v6/color-settings.htm (996 words)

	PlanetMath: weak* convergence in normed linear space
		"weak* convergence in normed linear space" is owned by bwebste.
		This is version 5 of weak* convergence in normed linear space, born on 2003-10-15, modified 2004-03-06.
		(Functional analysis :: Normed linear spaces and Banach spaces; Banach lattices :: Duality and reflexivity)
	planetmath.org /encyclopedia/WeakConvergenceInNormedLinearSpace.html (83 words)

	Time is Cubic, not Linear -- Cubic Awareness Online. (Site not responding. Last check: 2007-10-09)
		So, 2 space dimensions are occupied by the dynamic Day-Night duality (sunup, midday, sundown, midnight); and 1 space dimension is occupied by the static Polar duality (North and South poles).
		Time and Space are opposites, and so if we have a linear time dimension and a linear space dimension, then we'd expect them to be opposites.
		It's the same as with the space dimensions -- the Earth's rotational axis (a single linear space dimension) is separate from the two Space dimensions of the Equator plane.
	www.geocities.com /cubicprophecies/theory/timecubic.html (912 words)

	Non-linear Point Distribution Models
		By analysing the magnitude of the corresponding eigenvalues, the minimum dimensionality of the space on which the data lies can be calculated and the information loss estimated [2].
		This allows a non-linear training set to be projected into a linear space where PCA can be used to represent deformation.
		This is akin to the polygonal representation of a surface.
	homepages.inf.ed.ac.uk /rbf/CVonline/LOCAL_COPIES/BOWDEN1/bowden1.htm (2364 words)

	Union Bound for Linear Space-Time Codes (Site not responding. Last check: 2007-10-09)
		We address the general problem of linear code design for the quasi-static, flat-fading, coherent MIMO channel.
		A {\it linear code} refers to an encoder that is linear with respect to scalar input symbols.
		We provide a cohesive framework for analysis of linear codes in terms of a union bound on the {\it conditional} probability of symbol error.
	www.stanford.edu /group/wcs/abstractSandhu.html (178 words)

	CGTalk - Log VS Linear color space in production
		For those of you that don't know, linear colour space (such as RGB, CMYK) is not ideal for working with content that is to be broadcast on different media as the nature of linear colour space is very device dependent.
		Whereas logarithmic colour space (CIE XYZ) is more accurate since it correlates more similarly to the perception of colour by humans, and is therefore device independent.
		The whole issue of log vs. linear matters alot if you are trying to get the greatest possible dynamic range out of RGB data that is only sampled at 8 or 16 bits per channel.
	forums.cgsociety.org /printthread.php?t=60338 (904 words)

	Linear Algebra Glossary (Site not responding. Last check: 2007-10-09)
		Moreover, it is not enough that these vectors span the space; we also require that they be linearly independent, that is, there should be no redundant vectors in the set.
		The columns of an orthogonal matrix are an orthonormal basis for the linear space of vectors of dimension N.
		In such a case, there are no space advantages to be gained by using a special matrix storage format, and so the matrix entries are stored using the standard two dimensional array format provided by the programming language.
	www.csit.fsu.edu /~burkardt/papers/linear_glossary.html (13710 words)

	AIM: Bruce Fraser's appraisal
		Then, instead of repeating the linear-gamma moves in gamma-corrected space (which is the straw man on which Timo's examples rely), look at what it takes to achieve the same visual result in linear and in gamma-compensated space.
		In linear gamma, the pixel he forces to fl is at RGB level 1, 0, 0, so the result is visually insignificant.
		1.) Linear gamma spaces are unsuited to use of the USM filter, which relies on perceptual uniformity of the R, G, and B channels.
	www.aim-dtp.net /aim/evaluation/gamma_error/bruce_fraser.htm (855 words)

	Rosenberg, A Prosody of Space / Non-Linear Time
		It should be noted that in one dimension, space and time are nearly the same thing; however, in the more complex topologies of non-linear writing, as we shall see, space and time operate very differently.
		In this case linearity is so seriously fragmented that the reader may have an impression of the words disengaging from time altogether, such that prosody relationships become entirely spatial.
		One point worth noting here is that the concept of bonding strength--the attraction of two text elements across a real or imagined boundary--sounds quite symmetrical, whereas most hypertext links are one-directional.[7] But the directionality of the hypertext link is not really different from the directionality of time in conventional prosody.
	www.well.com /user/jer/10_3rosenberg.html (4903 words)

	A Linear Space Algorithm for Computing the Hermite Normal Form - Micciancio, Warinschi (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Abstract: Computing the Hermite Normal Form of an n andtimes; n matrix using the best current algorithms typically requires O(n 3 log M) space, where M is a bound on the length of the columns of the input matrix.
		Although polynomial in the input size (which is O(n 2 log M)), this space blow-up can easily become a serious issue in practice when working on big integer matrices.
		A linear space algorithm for computing the Hermite Normal Form.
	citeseer.lcs.mit.edu /micciancio01linear.html (572 words)

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