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# Topic: Tensor

###### In the News (Sun 16 Jun 19)

 What is a tensor? Tensors, defined mathematically, are simply arrays of numbers, or functions, that transform according to certain rules under a change of coordinates. A tensor may be defined at a single point or collection of isolated points of space (or space-time), or it may be defined over a continuum of points. A tensor may consist of a single number, in which case it is referred to as a tensor of order zero, or simply a scalar. www.physlink.com /Education/AskExperts/ae168.cfm   (0 words)

 PlanetMath: tensor   (Site not responding. Last check: ) A tensor is the mathematical idealization of a geometric or physical quantity whose analytic description, relative to a fixed frame of reference, consists of an array of numbers Examples of physical tensors are the energy-momentum tensor, and the polarization tensor. Actually, the tensor notion is quite general, and applies to all of the above examples; scalars and vectors are special kinds of tensors. planetmath.org /encyclopedia/Tensor.html   (850 words)

 Tensor - Wikipedia, the free encyclopedia Tensors may be written down in terms of coordinate systems, as arrays of scalars, but are defined so as to be independent of any chosen frame of reference. In the field of diffusion tensor imaging, for instance, a tensor quantity that expresses the differential permeability of organs to water in varying directions is used to produce scans of the brain. A tensor may be expressed as the sequence of values represented by a function with a vector valued domain and a scalar valued range. en.wikipedia.org /wiki/Tensor   (2204 words)

 PlanetMath: tensor array   (Site not responding. Last check: ) Tensors are widely used in science and mathematics, because these data structures are the natural choice of representation for a variety of important physical and geometric quantities. The theory of tensor arrays incorporates a number of other essential topics: basic tensors, tensor transformations, outer multiplication, contraction, inner multiplication, and generalized transposition. tensor arrays (The latter are used to represent quadratic forms.) Speaking idealistically, such objects should be typeset, respectively, as a column of column vectors and as a row of row vectors. planetmath.org /encyclopedia/TensorArray.html   (486 words)

 PlanetMath: tensor   (Site not responding. Last check: ) A tensor is the mathematical idealization of a geometric or physical quantity that may be represented relative to a given frame of reference as an array of numbers Examples of physical tensors are the energy-momentum tensor, and the polarization tensor. Actually, the tensor notion is quite general, and applies to all of the above examples; scalars and vectors are special kinds of tensors. www.planetmath.org /encyclopedia/Tensor.html   (852 words)

 Tensor (intrinsic definition) - Wikipedia, the free encyclopedia In differential geometry an intrinsic geometric statement may be described by a tensor field on a manifold, and then doesn't need to make references to coordinates at all. The tensors of rank zero are just the scalars (elements of the field F), those of contravariant rank 1 the vectors in V, and those of covariant rank 1 the one-forms in V* (for this reason the last two spaces are often called the contravariant and covariant vectors). Formally, this means that tensors were introduced as specific representations of the group of all changes of coordinate systems. en.wikipedia.org /wiki/Component-free_treatment_of_tensors   (971 words)

 Tensor product - Wikipedia, the free encyclopedia It means that if a pair of tensors are juxtaposed (placed side-by-side) then they combine by mere aggregation to form a new tensor which can be subsequently called the tensor product of the pair of juxtaposed tensors. Linear subspaces of the bilinear operators (or in general, multilinear operators) determine natural quotient spaces of the tensor space, which are frequently useful. Note that J's treatment also allows the representation of some tensor fields (as a and b may be functions instead of constants -- the result is then a derived function, and if a and b are differentiable, then a*/b is differentiable). en.wikipedia.org /wiki/Tensor_product   (964 words)

 [No title] This book works perfectly as a supplement to a course in tensor calculus, or as a quick reference for the various techniques and concepts involved, provided one is already somewhat familiar with the material. The question of the degrees of freedom of the tensor entries will be addressed, and a novel algorithm to compute the tensor by a linear technique is presented. An analysis of the error in the approximation of a generic trifocal tensor by the affine trifocal tensor is carried out and preliminary experiments with synthetic and real data show the reliability and robustness of the approximation under a wide range of conditions. www.lycos.com /info/tensor--imaging.html?page=4   (486 words)

 Maxima Manual - Tensor Tensor Package - will set to zero, in exp, all occurrences of the tensori that have derivative indices. Tensor Package - will set to zero, in exp, all occurrences of the differentiated object tensor that have n or more derivative indices as the following example demonstrates. Tensor package) This function first computes the covariant components LR[i,j] of the Ricci tensor (LR is a mnemonic for "lower Ricci"). www.ma.utexas.edu /maxima/maxima_27.html   (1080 words)

 tensor Vectors are tensors of dimension 1, matrices are of dimension 2. Tensors of a higher dimension can always be brought to a lower dimension if any of their extensions are 1. Multiply two tensors by first reordering the 'extensions' such that the extensions that are to be summed over are at the beginning of the list, and that these extensions match for both tensors. www.oroboro.com /rafael/docserv.php/index/projects/article/tensor   (2907 words)

 Time and Attendance, Access Control & Visitor Monitoring - Tensor Time Systems Inc Tensor is the leading manufacturer of smart card and key fob time and attendance, access control and visitor monitoring equipment and software. Tensor's smart card and key fob time and attendance system is called WinTA. Tensor smart cards use a proximity read method, reading through a wallet or purse in ¼ second (up to 15 times faster than magnetic swipe cards). www.tensor.com   (0 words)

 THE MEANING OF "TENSOR" Fortunately or unfortunately, the various meanings of "tensor" do actually have a commonality, so the problem becomes to recognize that commonality and also to disambiguate the different contextual meanings within that commonality. Properly, this the context of Tensor Analysis, analysis because it includes the concepts of differential and integral calculus. Tensor Product The tensor product grows from the idea of the "Cartesian Product" of the one dimensional x-axis as a vector space, and the one dimensional y-axis in elementary algebra to form the two dimensional Cartesian plane. graham.main.nc.us /~bhammel/MATH/tensor.html   (1952 words)

 Tensor   (Site not responding. Last check: ) Tensor President Don Gustafson said the press formatâs versatility and adaptability will always be a strong suit. The point of having a tensor theory is to explain the further implication of saying that a quantity is a tensor, beyond that specifying it requires a number of indexed components. This idea can then be further generalized to tensor fields, where the elements of the tensor are functionss, or even differentials. www.wikiverse.org /tensor   (1291 words)

 Pellionisz "Boston paper" 1987 Tensor Network Theory [9-10,19-22] is based on the axiom that neuronal networks trans-form generalized vectorial (tensorial) expressions of external invariants in intrinsic coordinates. Tensor network model of transformations of intrinsic coordinates: a model of the three-step vestibulo-collic head- stabilization sensorimotor reflex [23]. Tensors are mathematical operators connecting general coordinates, where one must distinguish between sensory- and motor-type vectorial representations (covariant and contravariant tensors, [20]). www.usa-siliconvalley.com /inst/pellionisz/boston87/boston87paper.html   (1522 words)

 Definition of Weyl tensor In differential geometry, the Weyl curvature tensor is the traceless component of the Riemann curvature tensor. The Weyl tensor has the special property that it is invariant under conformal changes to the metric. In dimension 3 the vanishing of the Cotton tensor is a necessary and sufficient condition for the Riemannian manifold being conformally flat. www.wordiq.com /definition/Weyl_tensor   (346 words)

 Tensor Personnel Software - Tensor plc   (Site not responding. Last check: ) The Tensor Personnel system is the culmination of over a decade of real world experience in the human resources and time and attendance sectors. Tensor Personnel is completely customisable, with the ability to bend, flex and adapt to changes in legislation, protocol, and the way in which your company operates. Tensor Personnel completely integrates with both the WinTA Lite and WinTA Enterprise time and attendance systems, but may also be used as a stand-alone application. www.tensor.com /us/tensor-personnel.htm   (528 words)

 ::: Tensor CS ::: Tensor can provide turnkey system design for corporations whose expertise does not reside in the electronic industry but are in need of an electronic device designed to provide a companion or support function to their product or service. Tensor can be integrated into your design team to generating technical specifications and descriptions of electronic hardware and or software required to fulfill your equipment requirements. Tensor has provided mechanical design interface capability to a number of excellent designers with capabilities spanning the traditional metal enclosures to those requiring various exotic configurations to meet the system design requirements. www.tensor-cs.com /index.html   (566 words)

 Tensor Voting Such a tensor can be visualized as an ellipse in 2-D, or an ellipsoid in 3-D. Intuitively, the shape of the tensor defines the type of information captured (point, curve, or surface element), and its size represents the saliency. A junction of two surfaces (a curve) is represented by a tensor in the shape of a circular disk (plate tensor) which is perpendicular to the curve's tangent. The stick component, which is parallel to the eigenvector corresponding to the largest eigenvalue and its magnitude (saliency) is equal to the difference of the largest and the second largest eigenvalue, encodes the likelihood of the point belonging to a smooth surface. homepages.inf.ed.ac.uk /rbf/CVonline/LOCAL_COPIES/MORDOHAI/tensorvoting.html   (1861 words)

 Tenser, said the Tensor The Xavier fans are forming an X, while I suspect that the gesture in the film is meant to refer to one of Orwell's famous fictional slogans of Ingsoc, "Freedom is Slavery". Geoff Pullum (after dropping the bombshell that he's moving to Edinburgh) recently wrote about the mayor of West Sacramento's announcement that he "want[s] to start thinking of gay as a verb and not just a noun". Tenser, said the Tensor is the blog of a graduate student in linguistics. tenser.typepad.com /tenser_said_the_tensor   (0 words)

 Tensor (Orbital) The rank is the number of dimensions needed as indices for the components of this tensor. Since every implementation is allowed to choose the tensor's internal data representation freely, you should not rely on such behaviour of mutable arithmetic objects to provoke inner state changes. The reason is that one-dimensional indices are meaningless for tensors of rank r>1 and that adding a single component to a tensor is not allowed as it would destroy its rectangular form. www.functologic.com /orbital/Orbital-doc/api/orbital/math/Tensor.html   (820 words)

 GiNaC: tensor.cpp File Reference The delta tensor is always symmetric and its trace is the dimension of the index space. A metric tensor with one covariant and one contravariant index is equivalent to the delta tensor. The Lorentz metric is a symmetric tensor with a matrix representation of diag(1,-1,-1,...) (negative signature, the default) or diag(-1,1,1,...) (positive signature). www.ginac.de /reference/tensor_8cpp.html   (342 words)

 tensor. The Columbia Encyclopedia, Sixth Edition. 2001-05   (Site not responding. Last check: ) Tensors appear throughout mathematics, though they were first treated systematically in the calculus of differential forms and in differential geometry. 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. www.bartleby.com /65/te/tensor.html   (170 words)

 Time Attendance, Access Control & Visitor Monitoring Software & Systems - Tensor plc Tensor is the leading manufacturer of Smart Card and Biometric Time and Attendance, Access Control, Visitor Monitoring, and Digital CCTV equipment and software. A system from Tensor is ideal for factory/office security, and comes complete with flexi-time and EU Working Time Directive software for accurate time and attendance results. Tensor smart cards use a proximity read method, reading through a wallet or purse in ¼ second (up to 15 times faster than magnetic swipe cards). www.tensor.co.uk /english   (627 words)

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