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	Einstein notation - Wikipedia, the free encyclopedia
		In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational convention useful when dealing with coordinate formulae.
		Abstract index notation is an improvement of Einstein notation.
		In Einstein notation, an index that is repeated twice in an equation implies a summation, and the summation symbol need not be included.
	en.wikipedia.org /wiki/Einstein_notation (771 words)

	Encyclopedia :: encyclopedia : Albert Einstein (Site not responding. Last check: 2007-11-01)
		Einstein divorced Mileva on February 14, 1919, and married his cousin Elsa Löwenthal (born Einstein: Löwenthal was the surname of her first husband, Max) on June 2, 1919.
		Einstein also assisted Erwin Schrödinger in the development of the quantum Boltzmann distribution, a mixed classical and quantum mechanical gas model although he realized that this was less significant than the Bose-Einstein model and declined to have his name included on the paper.
		Einstein began to form a generalized theory of gravitation with the Universal Law of Gravitation and the electromagnetic force in his first attempt to demonstrate the unification and simplification of the fundamental forces.
	www.hallencyclopedia.com /Albert_Einstein (12828 words)

	Mathematics - MSN Encarta
		Later, Einstein’s general theory of relativity (1915) extended special relativity to accelerated systems and showed gravity to be an effect of acceleration.
		Einstein’s discovery of relativity depended on studying objects in four dimensions, with time as the fourth dimension.
		Einstein hoped that a unified field theory could be found, and he worked on this project from 1928 until his death in 1955.
	encarta.msn.com /encyclopedia_761578291_1/Applied_Mathematics.html (1357 words)

	NationMaster - Encyclopedia: Gravitational lens (Site not responding. Last check: 2007-11-01)
		In physics, the Einstein field equation or Einstein equation is a differential equation in Einsteins theory of general relativity.
		It is usually referred to in the literature as an Einstein ring, since Chwolson did not concern himself with the flux or radius of the ring image.
		Einstein realized that it was also possible for astronomical objects to bend light, and that under the correct conditions, one would observe multiple images of a single source, called a gravitational lens or sometimes a gravitational mirage.
	www.nationmaster.com /encyclopedia/Gravitational-lens (3748 words)

	Tensor - Wikipedia, the free encyclopedia
		The notation was developed around 1890 by Gregorio Ricci-Curbastro under the title absolute differential calculus, and was made accessible to many mathematicians by the publication of Tullio Levi-Civita's 1900 classic text of the same name (in Italian; translations followed).
		In the 20th century, the subject came to be known as tensor analysis, and achieved broader acceptance with the introduction of Einstein's theory of general relativity, around 1915.
		A tensor may be expressed as the sequence of values represented by a function with a vector valued domain and a scalar valued range.
	www.wikipedia.org /wiki/Tensor (2237 words)

	einstein (Site not responding. Last check: 2007-11-01)
		Einstein on the Beach - Einstein on the Beach is an opera written by the minimalist composer Philip Glass and theatre director and designer Robert Wilson.
		Einstein notation - In mathematics, especially in applications of linear algebra to physics, the Einstein notation or Einstein summation convention is a notational co...
		Einstein (unit) - An einstein is a unit of irradiance, and is used in photochemistry.
	www.serebella.com /search/topic-einstein.html (765 words)

	Re: Teleparallelism; Einstein
		Einstein was dismayed and realized he owed some debt to Cartan, and he suggested some possibilities.
		In Einstein's letter to Cartan, Einstein also said: "I didn't at all understand the explanations you gave me in Paris; still less was it clear to me how they might be made useful for physical theory.
		Einstein was an outstanding man. This whole Cartan relationship is discussed by Michel Biezunski in his article "Inside the Coconut: The Einstein-Cartan Discussion on Distant Parallelism," in _Einstein and the History of General Relativity_, Edited by D. Howard and J. Stachel.
	www.lns.cornell.edu /spr/2002-01/msg0038021.html (925 words)

	Summation - Wikipedia, the free encyclopedia
		Here, i represents the index of summation; m is the lower bound of summation, and n is the upper bound of summation.
		One often sees generalizations of this notation in which an arbitrary logical condition is supplied, and the sum is intended to be taken over all values satisfying the condition.
		These degenerate cases are usually only used when the summation notation gives a degenerate result in a special case.
	en.wikipedia.org /wiki/sum (718 words)

	Why is c the symbol for the speed of light?
		By 1907 when Einstein switched from V to c in his papers, it had become the standard symbol for the speed of light in vacuum for electrodynamics, optics, thermodynamics and relativity.
		That was written in the United States, but the same notation was also found across Europe, from papers by Oliver Lodge [15] and Joseph Lamor [16] in England, to the lecture notes of Poincaré in France [17], and the textbooks of Paul Drude in Germany [18] and Lorentz in the Netherlands [19].
		Einstein mentioned to Stark that it was hard for him to find the time to read published scientific articles in order to acquaint himself with all the work others have done in the field, but he had seen papers by Lorentz, Kohn, Monsegeil and Planck [20].
	www.math.ucr.edu /home/baez/physics/Relativity/SpeedOfLight/c.html (4074 words)

	Curl - Wikipedia, the free encyclopedia
		Such notation involving operators is common in physics and C*-algebra.
		Although expressed in terms of coordinates, the result is invariant under proper rotations of the coordinate axes.
		In Einstein notation, with the Levi-Civita symbol it is written as:
	www.wikipedia.org /wiki/Curl (466 words)

	Tensor notation (Site not responding. Last check: 2007-11-01)
		The divergence theorem in vector and tensor notation...
		The equations of motion of a viscous fluid in tensor notation...
		Notation for General Relativity and Other Advanced Topics 75...
	www.scienceoxygen.com /math/517.html (118 words)

	E=mc⊃2
		Einstein's formula, which describes the relationship between energy (E), mass (m) and the speed of light (c), derives from Einstein's special theory of relativity.
		The formula E=mc² first appeared in an article by Einstein in 1905, using a different notation, and in 1907 he fully generalized the concept to the equivalence of mass and energy.
		The implication of the formula thus became that a small amount of matter could, in principle, be converted into a vast amount of energy.
	www.alberteinstein.info /gallery/gtext1.html (223 words)

	U Of Nevada Physicist Says Einstein Was A Plagiarist
		The Register - UK A theoretical physicist at the University of Nevada has published a paper alleging that Einstein did not derive the gravitational field equations at the heart of the General Theory of Relativity, and might in fact have copied key equations from fellow physicist David Hilbert.
		He compares the 'mutilated' document with published papers, and notes that certain forms of Hilbert's notation were only used by Einstein at a later date.
		Winterberg concludes that three people should be given credit for developing the general theory of relativity: Einstein, for recognising the shape of the problem, Grossmann for his insight that the contracted Riemann tensor was key to solving the problem, and Hilbert for completing the gravitational field theory equations.
	www.rense.com /general59/eins.htm (355 words)

	Einstein notation (Site not responding. Last check: 2007-11-01)
		In mathematics especially in applications of linear algebra to physics the Einstein notation or Einstein summation convention is a notational convention useful when with coordinate equations or formulas.
		In general relativity the Greek alphabet and the Roman alphabet are used to distinguish whether summing 1 2 3 or 0 1 2 (e.g.
		Perhaps more significantly the inner may be a primary object of study shouldn't be suppressed in the notation; this the case for example in general relativity.
	www.freeglossary.com /Einstein_notation (1445 words)

	Einstein notation -- For other topics related to Einstein see Einstein (disa... (Site not responding. Last check: 2007-11-01)
		Einstein notation -- For other topics related to Einstein see Einstein (disa...
		Furthermore, abstract index notation uses Einstein notation without requiring any range of values.
		In general relativity, the Greek alphabet and the Roman alphabet are used to distinguish whether summing over 1,2,3 or 0,1,2,3 (e.g.
	einstein-notation.en.tracking24.net (205 words)

	Tensor equations (Site not responding. Last check: 2007-11-01)
		Given a specified distribution of matter and energy in the form of a stress-energy tensor, the EFE are understood to be equations for the metric tensor g a b, as both the Ricci tensor and Ricci scalar...
		This section summarizes the notations of vector and tensor algebraic notations used to...
		where the Einstein curvature tensor is generated, through the gravitational coupling, by the matter stress-energy tensor.
	www.logicjungle.com /wiki/Tensor_equations (310 words)

	Einstein notation (Site not responding. Last check: 2007-11-01)
		In mathematics, especially in applications of linear algebra to physics, theEinstein notation or Einstein summation convention is a notational convention useful whendealing with coordinate equations or formulas.
		This vector wouldn't need to be given a specific name using only index notationeither, but the translation between the notations is easier to describe by giving it a name.
		Perhaps more significantly, the innerproduct may be a primary object of study that shouldn't be suppressed in the notation; this is the case, for example, in general relativity.
	www.therfcc.org /einstein-notation-43941.html (1184 words)

	Tensor notation (Site not responding. Last check: 2007-11-01)
		In this caseit represents a linear transformation, of rank one in the sense of linearalgebra - a clashing terminology that can cause confusion.
		Einstein summationconvention This states that in a product of two indexed arrays, if an index letter in the first is repeated in thesecond, then the (default) interpretation is that the product is summed over all values of the index.
		The Einstein convention is generally used in physics and engineeringtexts, to the extent that if summation is not applied it is normal to note that explicitly.
	www.therfcc.org /tensor-notation-133576.html (484 words)

	Talk:Tensor - InformationBlast
		While indicial notation is necessary for computation, it obscures the fact that tensors are invariant with respect coordinate systems, and that is one reason why they are useful.
		It is a fact of life, and it won't go away unless mathematicians present a compelling case to the engineering community to not use indicial notation.
		Indicial notation lends itself to writing computer programs, which are useful for making money doing stuff like predicting the subsurface flow of TCE (a nasty dry-cleaning slovent).
	www.informationblast.com /Talk:Tensor.html (5599 words)

	EMail Msg <199509210423.AAA10577@village.ios.com>
		People have experimented with integrated notations that capture all aspects, but they tend to be cluttered and awkward to work with -- lower level, in this sense.
		In fact, typical presentations of Z designs intersperse the formalism with English descriptions, graphical notations, etc. to help people understand the logic.
		The benefits of translating the design to a formal notation are that the exercise forces you to analyze carefully what you throught you meant, and of course the ability to reason about the resulting specification.
	www-ksl.stanford.edu /email-archives/srkb.messages/612.html (1104 words)

	The dreams that stuff is made of » 2004 » October
		As an interesting example, we could implement the generalized Einstein notation (as Synopsis 9 proposed, and everybody liked the idea, but nobody liked the solution).
		The index could be an autoöverloading value that computes its necessary range and then evaluates at all the values it needs to.
		The actual rules of Einstein notation are pretty yucky when you’re dealing in a practical context (it has to do with summing over things that appear exactly twice).
	www.luqui.org /blog/archives/2004/10 (562 words)

	Tensor (intrinsic definition) (Site not responding. Last check: 2007-11-01)
		This notation can somewhat obscure the fact that tensors are always cosets: manipulations performed via the representatives (v,w) must always be checked that they do not depend on the particular choice of representative.
		Another, alternate notation for this space is in terms of linear maps from a vector space V to a vector space W. Let
		is often used to denote the space of invertible linear transformations from V to W; however there is no analogous notation for tensor spaces.
	www.toshare.info /en/Tensor-modern.htm (1114 words)

	Glossary of tensor theory
		In this case it represents a linear transformation, of rank one in the sense of linear algebra - a clashing terminology that can cause confusion.
		Einstein notation This states that in a product of two indexed arrays, if an index letter in the first is repeated in the second, then the (default) interpretation is that the product is summed over all values of the index.
		The Einstein convention is generally used in physics and engineering texts, to the extent that if summation is not applied it is normal to note that explicitly.
	en.mcfly.org /Glossary_of_tensor_theory (548 words)

	Animal Einsteins: Number Crunchers
		To represent the number 1412, place one MandM placeholder in the 1000 column, four MandMs in the 100 column, One MandM in the 10 column and two MandMs in the 1 column.
		In expanded notation, this would be expressed as (1 x 1) = 1.
		Using your chart, figure out how to finish counting to 10 and write the answers on your paper, using both expanded notation and binary numbers.
	www.pbs.org /safarchive/4_class/45_pguides/pguide_903/4493_number.html (725 words)

	General relativity/Einstein Summation Notation - Wikibooks, collection of open-content textbooks
		All active members of Wikimedia projects are invited to vote in the 2006 Election to the Board of Trustees
		Mathematicians hate to write things, and are always on the look out for shortcuts that simplify their lives.
		Here are some more examples of the Einstein summation notation being used:
	en.wikibooks.org /wiki/General_relativity:Einstein_Summation_Notation (431 words)

	Definition of Covariant derivative
		Here we give a traditional index-notation introduction to the covariant derivative (also known as the tensor derivative) of a vector with respect to a vector field; the covariant derivative of a tensor is an extension of the same concept.
		Everywhere in this article we use Einstein notation.
		Often a notation is used in which the covariant derivative is given with a semicolon, while a normal derivative is indicated by a comma.
	www.wordiq.com /definition/Covariant_derivative (1404 words)

	Wigner
		The density matrix for the center of mass motion of the pair in (1.6) is a correlation function.
		The superfluid part of the Wigner phase space density, in special relativity notation, which is OK for pre-gravity micro-quantum gauge force and source “false vacuum”, is therefore,
		I now drop the cm subscript in the coordinate notation.
	www.stardrive.org /math2/Wigner.htm (386 words)

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