Tensors Tensors Abstract index notation is a mathematical notation for tensors and spinors, which uses indices to indicate their type. ...more on Wikipedia about "Abstract index notation"
In mathematics and theoretical physics, a tensor is antisymmetric on two indices i and j if it flips the sign if the two indices are interchanged: ...more on Wikipedia about "Antisymmetric tensor"
Tensors are frequently used in engineering to describe measured quantities. ...more on Wikipedia about "Application of tensor theory in engineering"
Tensors are used in various parts of physics, both as abstract constructs in mathematical physics and for describing relations between quantities represented by matrices. ...more on Wikipedia about "Application of tensor theory in physics"
In physics and mathematics, axiality and rhombicity are two characteristics of a symmetric second-rank tensor in three-dimensional Euclidean space, describing its directional asymmetry. ...more on Wikipedia about "Axiality and rhombicity"
In linear algebra, one associates a polynomial to every square matrix, its characteristic polynomial or secular equation. This polynomial encodes several important properties of the matrix, most notably its eigenvalues, its determinant and its trace. ...more on Wikipedia about "Characteristic polynomial"
A tensor is a generalization of the concepts of vectors and matrices. Tensors allow one to express physical laws in a form that applies to any coordinate system. For this reason, they are used extensively in continuum mechanics and the theory of relativity. ...more on Wikipedia about "Classical treatment of tensors" I wish I had a shortopedia.
Effect of torsion tensor on the Christoffel symbol and the spin connection. ...more on Wikipedia about "Contortion tensor"
In mathematics and theoretical physics, covariance and contravariance are concepts used in many areas, generalising in a sense invariance, i.e. the property of being unchanged under some transformation. In mathematical terms they occur in a foundational way in linear algebra and multilinear algebra, differential geometry and other branches of geometry, category theory and algebraic topology. In physics they are important to the treatment of vectors and other quantities, such as tensors, that have physical meaning but are not scalars. Both special relativity ( Lorentz covariance) and general relativity ( general covariance) use covariant basis vectors. ...more on Wikipedia about "Covariance and contravariance"
In mathematics, a covariant transformation is a rule (specified below), that describes how certain physical entities change under a change of coordinate system. ...more on Wikipedia about "Covariant transformation"
In mathematics, the De Rham complex is the cochain complex of exterior differential forms on some smooth manifold, with the exterior derivative as differential. See de Rham cohomology. ...more on Wikipedia about "De Rham complex"
A differential form is a mathematical concept in the fields of multivariate calculus, differential topology and tensors. The modern notation for the differential form, as well as the idea of the differential forms as being the wedge products of exterior derivatives forming an exterior algebra, was introduced by Elie Cartan. ...more on Wikipedia about "Differential form"
Diffusion tensor imaging (DTI) is a method for imaging the fibrous structure of organs in the body, such as the brain, using the diffusivity of water. It involves the multidimensional assessment of diffusion data in vivo by representing diffusion in terms of tensors. DTI is a development of diffusion MRI. ...more on Wikipedia about "Diffusion tensor imaging"
In mathematics, in particular multilinear algebra, the dyadic product ...more on Wikipedia about "Dyadic product" Please visit again http://www.shortopedia.com Tensors
A dyadic tensor in multilinear algebra is a second rank tensor written in a special notation, formed by juxtaposing pairs of vectors, i.e. placing pairs of vectors side by side. ...more on Wikipedia about "Dyadic tensor"
:For other topics related to Einstein, see Einstein (disambiguation). ...more on Wikipedia about "Einstein notation"
In differential geometry, the Einstein tensor is a 2-tensor defined over Riemannian manifolds. In index-free notation it looks like this ...more on Wikipedia about "Einstein tensor"
The electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor or Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field of a physical system in Maxwell's theory of electromagnetism. ...more on Wikipedia about "Electromagnetic tensor"
In continuum mechanics, finite deformation tensors are tensors that are used to measure deformation. They are used when the deformation is not small, as is commonly the case in mechanics of rubber, plastics and viscoelastic fluids. For small deformations see strain tensor. ...more on Wikipedia about "Finite deformation tensors"
This is a glossary of tensor theory. For expositions of tensor theory from different points of view, see: ...more on Wikipedia about "Glossary of tensor theory"
:Note: The following is a modern component-based treatment of tensors (sometimes called the "classical treatment" of tensors). Read the article tensor for a simple description of tensors, or see the component-free treatment of tensors for a more abstract treatment. For an even more traditional approach, see classical treatment of tensors. ...more on Wikipedia about "Intermediate treatment of tensors"
In mathematics, in the fields of multilinear algebra and representation theory, invariants of tensors are coefficients of characteristic polynomial of the tensor A: ...more on Wikipedia about "Invariants of tensors"
In mathematics, the Kronecker delta or Kronecker's delta, named after Leopold Kronecker ( 1823- 1891), is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. So, for example, , but . It is written as the symbol δij, and treated as a notational shorthand rather than as a function. ...more on Wikipedia about "Kronecker delta"
In mathematics, the Laguerre form is generally given as a third degree tensor-valued form, that can be written as, ...more on Wikipedia about "Laguerre form"
There are two different tensors sometime referred to as the Lanczos tensor (both named after Cornelius Lanczos): ...more on Wikipedia about "Lanczos tensor" www.shortopedia.com never sleeps.
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