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Topic: Hamel dimension

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	NationMaster - Encyclopedia: Hamel dimension
		In mathematics, the dimension of a vector space V is the cardinality (i.e.
		The length of a module and the rank of an abelian group both have several properties similar to the Hamel dimension of vector spaces.
		The dimension of a vector space V is the cardinality (i.e.
	www.nationmaster.com /encyclopedia/Hamel-dimension (606 words)

	NationMaster - Encyclopedia: 2D
		Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space.
		In the SI system, the dimension is given by the seven exponents of the fundamental quantities.
		The Krull dimension of a commutative ring, named after Wolfgang Krull (1899 - 1971), is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring.
	www.nationmaster.com /encyclopedia/2D (884 words)

	Wikinfo \| Dimension (Site not responding. Last check: 2007-10-07)
		Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space.
		Time is frequently referred to as the "fourth dimension"; time is not the fourth dimension of space, but rather of spacetime.
		The Krull dimension of a commutative ring is defined to be the maximal length of a strictly increasing chain of prime ideals in the ring.
	www.wikinfo.org /wiki.php?title=Dimension (654 words)

	Kids.Net.Au - Encyclopedia > Hamel dimension
		It is sometimes called Hamel dimension when it is necessary to distinguish it from other types of dimension.
		The Hamel dimension is a natural generalization of the dimension of Euclidean space, since E
		However, the Hamel dimension depends on the base field, so while R has dimension 1 when considered as a vector space over itself, it has dimension c (the cardinality of the continuum) when considered as a vector space over Q (the rationals).
	www.kids.net.au /encyclopedia-wiki/ha/Hamel_dimension (198 words)

	UFO Encounter Fuels 30-Yr Quest For Magnetic Energy
		They brought Hamel aboard their flying saucer - "They sent me through the roof!" is how he describes the paranormal out-of-body experience - where their androgynous android companion, On, illustrated how they travelled from their distant galaxy to Earth: their ship floated in an anti-gravity bubble powered by electrically charged vortical airflow between magnetic rings.
		Hamel received a breathtaking fifteen-minute demo ride at hypersonic speed over the Canadian landscape, pausing only to hover over a man carrying a yoke laden with two buckets, who collapsed when he saw the ship overhead.
		Hamel has been living on the brink of Armageddon for as long as he can remember, and he's not about to wait for you to come around before trying to build a magnetic free-energy device that he believes can save the world from the tyranny of the Grid.
	www.rense.com /general58/UFOencounterfuels30yr.htm (3007 words)

	PlanetMath: Banach spaces of infinite dimension do not have a countable Hamel basis (Site not responding. Last check: 2007-10-07)
		A Banach space of infinite dimension does not have a countable Hamel basis.
		In fact, the Hamel dimension of an infinite-dimensional Banach space is always at least the cardinality of the continuum (even if the Continuum Hypothesis fails).
		This is version 18 of Banach spaces of infinite dimension do not have a countable Hamel basis, born on 2005-01-31, modified 2006-12-27.
	planetmath.org /encyclopedia/ABanachSpaceOfInfiniteDimensionDoesntHaveACountableAlgebraicBasis.html (510 words)

	Dimension
		In mathematics, dimensions are the parameters required to describe the position and relevant characteristics of any object within a conceptual space —where the dimensions of a space are the total number of different parameters used for all possible objects considered in the model.
		In the physical sciences and in engineering, the dimension of a physical quantity is the expression of the class of physical unit that such a quantity is measured against.
		The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that n+1-dimensional balls have n dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets.
	articles.gourt.com /en/Dimension (1660 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: 2007-10-07)
		In mathematics, dimensions are the parameters required to describe the position and relevant characteristics of any object within a conceptual space —where the dimensions of a space are the total number of different parameters used for all possible objects considered in the model.
		The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that n+1-dimensional balls have n dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets.
		The negative (fractal) dimension is introduced by Benoit Mandelbrot, in which, when it is positive gives the known definition, and when it is negative measures the degree of "emptiness" of empty sets.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Dimension (1558 words)

	Dimension (vector space) - Biocrawler (Site not responding. Last check: 2007-10-07)
		It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension.
		The dimension of the vector space V over the field F is written as dim
		Any two vector spaces over F having the same dimension are isomorphic.
	www.biocrawler.com /encyclopedia/Hamel_dimension (468 words)

	Dimension information - Search.com
		Adding the three Euler angles, for a total 6 dimensions, allows the current degrees of freedom —orientation and trajectory —of the airplane to be known.
		The most well-known treatment of time as a dimension is Einstein's theory of general relativity, which treats perceived space and time as parts of a four-dimensional manifold.
		The theory of manifolds, in the field of geometric topology, is characterised by the way dimensions 1 and 2 are relatively elementary, the high-dimensional cases n > 4 are simplified by having extra space in which to 'work'; and the cases n = 3 and 4 are in some senses the most difficult.
	www.search.com /reference/Dimension (1877 words)

	More on Dimension
		In physics, the dimension of a quality is the expression of that quality in basic units: the dimension of speed, for example, is length divided by time.
		In the SI system, the dimension is given by the seven exponents of the fundamental quantities.
		All, however, are ultimately based on the concept of the dimension of Euclidean n-space E n.
	www.artilifes.com /dimension.htm (872 words)

	Dimension Summary
		It is perceived differently from the three spatial dimensions in that there is only one of it, and that movement seems to occur at a fixed rate and in one direction.
		The theory of manifolds, in the field of geometric topology, is characterized by the way dimensions 1 and 2 are relatively elementary, the high-dimensional cases n > 4 are simplified by having extra space in which to 'work'; and the cases n = 3 and 4 are in some senses the most difficult.
		Science fiction texts often mention the concept of dimension, when really referring to parallel universes, alternate universes, or other planes of existence, or concepts that are beyond the reader.
	www.bookrags.com /Dimension (3541 words)

	AIAA - Aerospace America Online - AN AEROSPACE FORCE TAKES SHAPE - The USAF is reshaping itself into an aerospace ...
		Michael A. Hamel, director of space operations and integration on the air staff at the Pentagon.
		Ryan had foreshadowed the Air Force’s adoption of the "aerospace force" designation: In 1997 he noted that he preferred it to "air and space force," the name then in favor, because it more accurately denoted the seamless integration of air and space.
		The integration of air and space "will present new opportunities for aerospace forces to maneuver within the entire vertical dimension and provide an array of long-range air and space capabilities," the document predicts.
	www.aiaa.org /aerospace/Article.cfm?issuetocid=60&ArchiveIssueID=10 (3359 words)

	Mattress Dimension
		Dimension (from Latin "measured out") is, in essence, the number of degrees of freedom available for movement in a space.
		It is conventional(and for most practical purposes entirely sensible) to consider this as three spatial dimensions and one of time.
		It is somewhat different to the three spatial dimensions in that there isonly one of it, and movement seems to be possible in only one direction.
	www.altvetmed.com /face/16933-mattress-dimension.html (568 words)

	An Interview With Gary Hamel
		In 1994, when Gary Hamel co-authored "Competing for the Future" (Harvard Business School Press) with his long-time friend, collaborator and former professor, C.K. Prahalad, it was something of a publishing event.
		Hamel, who is 43 years old, has continued his writing and speaking activities and has also founded a consulting firm called Strategos.
		Hamel argues, "is an unwillingness or inability to look outside of current experiences." Helping companies cure that type of blindness has been the latest focus of his work.
	www.strategy-business.com /press/16635507/13304 (5616 words)

	Kotonline
		The Hamel ElastoTwister LE has a modern construction in sections and consists of a drive unit, the transmission headstock and the aligned sections, called spindle fields.
		The weaving texture makes the material appear smooth and elegant on the outside and, thanks to the Hamel covering yarn, but it has a soft feel on the inside which is pleasant for the skin and offers a high degree of wearing comfort.
		The Hamel ElastoTwister 125 LE is used in the first process step and the Allma FET 160 in the second one.
	www.kotonline.com /english_pages/ana_basliklar/hamel.asp (4923 words)

	Flying Blind? - CIOs need to start thinking about customers as much as cost-cutting
		Instead of advocating a top-down approach, Hamel, who is also a visiting professor of strategic and international management at the London Business School, and Prahalad, a professor at the University of Michigan, proposed that business strategy should involve employees at all levels of a company.
		The reason for that blindness, Hamel says: "An unwillingness or inability to look outside of current experiences." Helping companies "see" better has been the focus of his latest work.
		Hamel recently spoke with CIO Insight Executive Editor Marcia Stepanek about how CIOs contribute to that blindness—and how they can correct their vision.
	www.cioinsight.com /print_article2/0,1217,a=12813,00.asp (3853 words)

	The Dispatch - Serving the Lexington, NC - News (Site not responding. Last check: 2007-10-07)
		In mathematics, the dimension of a vector space V is the cardinality (i.e.
		It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension.
		Some simple formulae relate the dimension of a vector space with the cardinality of the base field and the cardinality of the space itself.
	www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Hamel_dimension (479 words)

	Leader to Leader Institute Leader to Leader: Winter 2003
		Across the globe and in every industry and sector of society, the old saying is more true than ever -- the only constant is change.
		Gary Hamel [complete text of article] -- "the world's reigning strategy guru," according to the Economist -- tackles head on the new competitive landscape in the post-bubble economy.
		John Kotter [complete text of article], world-renowned leadership expert at the Harvard Business School, also does not mince words.
	www.pfdf.org /knowledgecenter/L2L/winter2003/editors.html (591 words)

	The world's top dimension websites
		Some theories predict that the space we live in has in fact many more dimensions (frequently 10, 11 or 26) but that the universe measured along these additional dimensions is subatomic in size.
		This does not have a Euclidean geometry, so temporal directions are not entirely equivalent to spatial dimensions.
		The Krull dimension of a commutative ring is defined to be the maximal number of strict inclusions in an increasing chain of prime ideals in the ring.
	www.websbiggest.com /wiki-article-tab.cfm/dimension? (782 words)

	Math Forum Discussions
		Is it true, using AC, that if a vector space has infinite
		Hamel dimension m, then the dual has Hamel dimension 2^m ?
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /kb/thread.jspa?messageID=4853845&tstart=0 (160 words)

	Qui sommes-nous ? - Distrijob.fr - Emploi et job Grande distribution et Distribution spécialisée
		Ce site a été créé en 2000 par des professionnels de la distribution, avec pour ambition d'offrir un moyen simple, rapide et efficace pour mettre en relation les candidats et les employeurs des métiers de la distribution.
		En 2005, le site initial a changé de nom pour s'appeler Distrijob.fr, afin d'apporter dans le nom même du site, une dimension "emploi" absente jusqu'alors, positionnant ainsi immédiatement notre activité aux yeux des internautes.
		En connaissance de cause, nous savons pourtant que les métiers offerts sont passionnants, avec une vraie dimension managériale et technique, à tous les niveaux de la hiérarchie.
	www.distrijob.fr /home/qui.asp (342 words)

	MathLinks Math Forums :: View topic - Hamel dimension
		MathLinks Math Forums :: View topic - Hamel dimension
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	www.mathlinks.ro /Forum/viewtopic.php?p=938370 (207 words)

	INTJ Profile
		We may catch a glimpse of it in the unspoken attitude of good will, or the gracious smile or nod.
		Some question the existence of Feeling in this type, yet its unseen balance to Thinking is a cardinal dimension in the full measure of the INTJ's soul.
		Sensing serves with a good will, or not at all.
	www.typelogic.com /intj.html (1087 words)

	dimension
		Time is also thought of as a dimension; indeed, in relativity theory and as a component of spacetime, it is treated almost exactly the same as a dimension of space.
		There are, for example, Hamel dimensions, Lebesgue covering dimensions, and Hilbert spaces.
		So-called Hausdorff dimensions are used to characterize fractals – mathematical objects that have fractional dimensions – by giving a precise meaning to the idea of how well something, such as an extremely "wriggly" curve or surface, fills up the space in which it is embedded.
	www.daviddarling.info /encyclopedia/D/dimension.html (285 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-07)
		In fact, the dimension of a Hilbert space is the cardinality of an arbitrary orthonormal basis in it.
		This dimension is sometimes referred to as the Hilbert dimension (as distinct from the linear dimension of a Hilbert space, i.e.
		The concept of a dimension is connected with that of the deficiency of a Hilbert subspace, also called the codimension of a Hilbert subspace.
	eom.springer.de /H/h047380.htm (2478 words)

	Gary Hamel - International Strategy Guru, Author of Leading the Revolution - Nationwide Speakers Bureau
		Hamel also advises national leaders on matters of innovation policy, entrepreneurship and industrial competitiveness.
		At present, Hamel is leading an effort at the London Business School to build the world’s first “Management Innovation Lab.” The Lab is a pioneering attempt to create a setting in which progressive companies and world renowned management scholars work together to co-create “tomorrow’s best practices” today.
		Hamel received his Ph.D. from the University of Michigan and has held faculty appointments at the U. of M. and Harvard Business School.
	www.nationwidespeakers.com /speaker/505 (468 words)

	Dialog on Leadership: Presencing: Learning From the Future As It Emerges
		A third and more subtle dimension of change has to do with the increasing relevance of experience, awareness and consciousness and their underlying driving force, the process of spiritualization (Conlin 1999) or, to use a less distracting term, the process of becoming aware of one’s more subtle experiences (Depraz, Varela and Vermersch, 1999).
		Thus the blind spot Gary Hamel is pointing at is the blind spot of cognition 3 and 4.
		But the principle of intention and will adds another dimension: as intention and will quicken and crystallize, the result is a transformation of one’s identity from victim to co-creator through whom new worlds are being brought to the fore.
	www.dialogonleadership.org /Presencing00.html (11766 words)

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