TENSOR

in mathematics, quantity that depends linearly on several vector variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates). Tensors appear throughout mathematics, though they were first treated systematically in the calculus of differential forms and in differential geometry. They play an important role in mathematical physics, particularly in the theory of relativity. Tensors are also important in the theory of elasticity, where they are used to describe stress and strain. The study of tensors was formerly known as the absolute differential calculus but is now called simply tensor analysis.

See R. Abraham et al., Manifolds, Tensor Analysis, and Applications (1988).

____________________

The Columbia Encyclopedia, Sixth Edition Copyright© 2004, Columbia University Press. Licensed from Lernout & Hauspie Speech Products N.V. All rights reserved.

-46859-

Top...
Search the Library
Books
Journals
Magazines
Newspapers
Encyclopedia
Advanced Search
About Questia
Questia is the world's largest online academic library offering full-text books, journals, and articles on thousands of topics.

Join Now...
Questia Books and Articles on: Tensor
We found: 685 results
By media type:
 

Books:

 

488  

 

Journal articles:

 

158  

 

Magazine articles:

 

15  

 

Newspaper articles:

 

16  

 

Encyclopedia articles:

 

8  
 

books on: Tensor  - 488 results

       More book Results: 1-10 11-20 21-30 31-40 41-50 >>  
 
1.
Tensors and Manifolds: With Applications to Mechanics and Relativity
Book by Robert H. Wasserman; Oxford University Press, 1992
Subjects: Calculus Of Tensors, Generalized Spaces, Manifolds (Mathematics), Mathematical Physics, Mechanics, Relativity (Physics)
...6. Suppose A is a tensor of type 0, 4 having...if B and C are two tensors having the given symmetries...Let b be a symmetric tensor of type 0, 2 . Then...V = n , then a 0, 4 tensor with the symmetries of...the spaces of covariant tensors. It will be evident...
2.
International Dictionary of Physics and Electronics
Book by Walter C. Michels; Van Nostrand, 1956
...COVARIANT. See tensor, contravariant...for covariant tensors of rank one and...like a covariant tensor of rank two...contravariant and mixed tensors of all ranks may...law for a mixed tensor of second rank is . Mixed tensors of higher rank...
3.
Introduction to the Theory of Relativity
Book by Peter Gabriel Bergmann; Prentice-Hall, 1947
Subjects: Relativity (Physics)
...vector calculus by introducing in addition to tensors a new type of quantity, the " tensor densities ." The tensor densities transform like tensors, except that they are also multiplied by the...
4.
Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society: August 13-16, 1994, Cognitive Science Program, Georgia Institute of Technology
Book by Cognitive Science Society (U.S.); Lawrence Erlbaum Associates, 1994
Subjects: Artificial Intelligence--Congresses, Cognition--Congresses, Cognitive Neuroscience--Congresses, Cognitive Science--Congresses, Computational Linguistics--Congresses
...index, as in Ti. Tensor product representations...structures require tensors of rank higher than...and v are rank 1 tensors--regard them as column vectors--the tensor product is the same...of the resulting tensor is the sum of the...elements of the addend tensors. Two tensors may...
5.
Cognitive Dynamics: Conceptual and Representational Change in Humans and Machines
Book by Eric Dietrich, Arthur B. Markman; Lawrence Erlbaum Associates, 2000
Subjects: Cognitive Science, Mental Representation, Thought And Thinking
...detailed consideration. A tensor product is an outer product...example, in the case of a tensor, ab, formed from vectors...Fig. 9.1 : abij = aibj. 1 Tensors can be formed from any number...this way. For instance, a tensor can be formed from three vectors...
More book Results: 1-10 11-20 21-30 31-40 41-50 >>

Top...
 

journal articles on: Tensor  - 158 results

       More journal Results: 1-10 11-20 21-30 31-40 41-50 >>  
 
1.
Using Magnetic Resonance Imaging and Diffusion Tensor Imaging to Assess Brain Damage in Alcoholics
Journal article by Margaret Rosenbloom, Edith V. Sullivan, Adolf Pfefferbaum; Alcohol Research & Health, Vol. 27, 2003
...Magnetic Resonance Imaging and Diffusion Tensor Imaging to Assess Brain Damage in Alcoholics...A new MR technique called diffusion tensor imaging (DTI) can aid in detecting the...magnetic resonance imaging; diffusion tensor imaging; brain imaging; patient assessment...
2.
Using Magnetic Resonance Imaging and Diffusion Tensor Imaging to Assess Brain Damage in Alcoholics
Journal article by Margaret Rosenbloom, Edith V. Sullivan, Adolf Pfefferbaum; Alcohol Research and Health, Vol. 27, 2003
Subjects: Alcohol use, Alcoholism, Brain damage, Brain research, Cognition & reasoning, Motor ability, Nuclear magnetic resonance--NMR
...Magnetic Resonance Imaging and Diffusion Tensor Imaging to Assess Brain Damage in Alcoholics...and its constituent parts. Diffusion tensor imaging (DTI) reveals the integrity...measure gross brain neuroanatomy. Diffusion tensor imaging makes use of the fact that water...
3.
From Small-scale Faults to Plate Kinematics: Palaeostress Determinations in a Fragmented Arc Complex (Se Livingston Island, S Shetlands, Antarctica)
Journal article by P. Santanach, R. Pallas, F. Sabat, J. A. Munoz; Journal of the Geological Society, Vol. 153, 1996
Subjects: Geology, Islands, Livingston Island, Plate tectonics
...calculated for every stress tensor. Among all stress tensors the one yielding a minimum...establish two additional stress tensors (tensor 2: sigma^sub 1^ =13...characterized by stress tensors 1, 2 and 3. Tensor I corresponds to a strike...
4.
Separation of Multiple Stress Events by Fault Striation Analysis: an Example from Variscan and Younger Structures at Ogmore, South Wales
Journal article by Richard J. Lisle, Sara Vandycke; Journal of the Geological Society, Vol. 153, 1996
Subjects: Geology, Sediments, Stone
...method yielded four tensors A-D (Fig 9): tensor A has an orientation...Unlike the best-fit tensor computed for all of the faults at site 2, the tensors A-D account well...yield four stress tensors. Tensor A has a gently plunging...
5.
Magnetotelluric Constraints on the Tectonic Setting of Grenville-aged Orogenesis in Central Australia
Journal article by K. M. Selway, M. Hand, J. L. Payne, G. S. Heinson, A. Reid; Journal of the Geological Society, Vol. 168, 2011
Subjects: Boundaries, Geology, Plate tectonics
...1D or 2D. The phase tensor is characterized by three...1 is a measure of the tensors relationship to the coordinate...phase values. The phase tensor is commonly represented...enough to affect the phase tensors, which suggest that...Modelling The phase tensor analysis showed that...
More journal Results: 1-10 11-20 21-30 31-40 41-50 >>

Top...
 

magazine articles on: Tensor  - 15 results

       More magazine Results: 1-10 11-15 >>  
 
1.
Piece of Mind
Magazine article by Aileen Constans; The Scientist, Vol. 17, January 27, 2003
...Irvine, Calif.-based Tensor Biosciences havent created...says Miro Pastrnak, Tensors director of business...at different sites. Tensor has increased the systems...to produce signals. Tensor has developed methods...levels. Pastrnak says Tensors technology fills an unmet...
2.
Aaai 2007 Spring Symposium Series Reports
Magazine article by Thomas Barkowsky, Peter Bruza, Zachary Dodds, Oren Etzioni, George Ferguson, Piotr Gmytrasiewicz, Bernhard Hommel, Benjamin Kuipers, Rob Miller, Leora Morgenstern, Simon Parsons, Holger Schultheis, Adriana Tapus, Neil Yorke-Smith; AI Magazine, Vol. 28, Fall 2007
...recovering many powerful results from quantum mechanics and tensor and lattice operators that generate representations for sophisticated...the centrality of vector representations and the use of the tensor product to create joint or combined distributions in both theories...
3.
Aaai News
Magazine article; AI Magazine, Vol. 27, Fall 2006
Subjects: American Association for Artificial Intelligence, Artificial intelligence, Homeopathic medicine, Intelligent agents, Scholarships & fellowships, Software
...Chicago, Illinois) * Three-Dimensional Face Recognition from Video: Facial Surface Re- construction and Analysis Using Tensor Algebra and Differential Geometry (Justin Moore Solomon, Thomas Jefferson High School for Science and Technology, Alexandria...
4.
The Commitment of an Intellectual: Paul M. Sweezy (1910-2004)
Magazine article by John Bellamy Foster; Monthly Review, Vol. 56, October 2004
Subjects: Economists--Biography, Sweezy, Paul M.--Biography
...molecules, it is an electromagnetic field, it is a spatio-termporal region (a class of events) with a particular curvature tensor. Each answer has to be thought of as a particular coding of the pen. The pen itself is what is common to all these codings...
5.
Blue Door
Magazine article by Sarah Hart, Tanya Barfield; American Theatre, Vol. 23, December 2006
Subjects: Barfield, Tanya, Dramatists, Playwrights
...Leroy, who is calling whom a nigger? (Returning to the lesson) Very well. When Kurt Godel added rotation to the stress tensor, here, he found a-- "Nigger." Leroy! Open the book, open my book. Do you think--if you were to open one goddamn...
More magazine Results: 1-10 11-15 >>

Top...
 

newspaper articles on: Tensor  - 16 results

       More newspaper Results: 1-10 11-16 >>  
 
1.
A Breath of Fresh Air; Scenic: Views of Blencathra in Cumbria. Inset: The Field Centre
Newspaper article; The Daily Mail (London, England), August 27, 2007
...someone explain Riemanns metric tensor, something I failed to grasp...is very unlikely to have met tensors in school mathematics and most...encounter them. The Riemann metric tensor is a mathematical device for...difficulty in coming to grips with tensors and had to seek help from the...
2.
Aptargroup Starts Realignment
Newspaper article; Daily Herald (Arlington Heights, IL), February 13, 2010
Subjects: AptarGroup Inc., Metal products industry, Metalworking industry, Sparton Corp., Telecommunications equipment industry
...within 14 minutes of the scheduled arrival time. Tensor ships to publication WOODRIDGE -- Tensor Group Inc. said Friday it will ship three web...Presse de la Manche of Cherbourg, France. The Tensor T-400 4-high towers will replace two existing...
3.
A Breath of Fresh Air; Scenic: Views of Blencathra in Cumbria. Inset: The Field Centre
Newspaper article; The Daily Mail (London, England), August 27, 2007
...someone explain Riemanns metric tensor, something I failed to grasp...is very unlikely to have met tensors in school mathematics and mostmathematics...encounter them. The Riemann metric tensor is a mathematical device for...difficulty in coming to grips with tensors and had to seek helpfrom the...
4.
Media Wales Reader Offer
Newspaper article; South Wales Echo (Cardiff, Wales), March 1, 2010
...Box 300, Rochester, Kent, ME2 2HJ Cheques made payable to: Tensor Marketing Ltd. Please allow up to 28 days delivery. STONE...order for pounds _____________ made payable to: Tensor Marketing Ltd or please debit my Maestro/Mastercard/Visa...
5.
The 50 Fastest Growing Firms
Newspaper article; The Journal (Newcastle, England), September 28, 2005
...mechanical and building construction. The firm was founded in 1997 and employs about 100 staff. Tensor Marketing Limited Founded in 1974, Darlington-based Tensor Marketing Ltd and the Factory Shop supply household products to the mail order industry...
More newspaper Results: 1-10 11-16 >>

Top...
 

encyclopedia articles on: Tensor  - 8 results

       More encyclopedia Results: 1-8 >>  
 
1.
Tensor
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2009
TENSOR in mathematics, quantity...Cartesian coordinates ). Tensors appear throughout mathematics...theory of relativity . Tensors are also important...strain. The study of tensors was formerly known...is now called simply tensor analysis. See R...
2.
Levi-Civita, Tullio
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2009
...Rome (1919 38) and was noted for his researches in pure geometry, hydrodynamics, celestial mechanics, and tensor analysis (see tensor ), on which Einsteins work depended in part. He wrote Simplified Presentation of Einsteins Unified Field Equations...
3.
Differential Geometry
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2009
...theory of surfaces are expressed most easily in the notation of tensors . It is found that the total, or Gaussian, curvature of a...formulated entirely in terms of the differential geometry, in tensor notation, of a four-dimensional manifold combining space...
4.
Hamilton, Sir William Rowan
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2009
...believed this work to be his most important, quaternions have been superseded in many applications by the methods of vector and tensor analysis. Of some import, however, was his discovery that the algebra of quaternions does not follow the commutative law...
5.
Analysis
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2009
...variable analysis, in which the variables are of the form z = x + iy, where i is the imaginary unit; vector analysis and tensor analysis; differential geometry ; and many other fields. ____________________ Copyright 2009 Columbia University...
More encyclopedia Results: 1-8 >>

Top...
 About Questia   ::   Privacy   ::   Contact