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- Using of [[Invariant theory|invariant polynomial tensors]] in [[Cartesian coordinate system|Cartesian coordinates]], as shown in a n ...oordinates]] are not involved here. The rules for using harmonic symmetric tensors are demonstrated that directly follow from their properties. These rules ar ...28 KB (4,317 words) - 05:16, 27 January 2025
- ...r infinitesimal deformations and rotations, the Cauchy and Piola–Kirchhoff tensors are identical. ...P}</math> is one possible solution to this problem. It defines a family of tensors, which describe the configuration of the body in either the current or the ...4 KB (594 words) - 18:36, 28 November 2024
- ...}}</ref> Some useful relations in the algebra of vectors and second-order tensors in curvilinear coordinates are given in this section. The notation and con ===Second-order tensors in curvilinear coordinates=== ...57 KB (9,439 words) - 15:08, 10 October 2024
Page text matches
- ...st3=A. W.-C.|last3=Lun|title=The classification of the Ricci and Plebanski tensors in general relativity using Newman-Penrose formalism|journal=J. Math. Phys. [[Category:Tensors]] ...2 KB (229 words) - 03:55, 31 March 2023
- ===Parallel Tensors=== An example for recurrent [[Tensor field|tensor]]s are parallel tensors which are defined by ...5 KB (696 words) - 10:44, 17 January 2025
- ...r infinitesimal deformations and rotations, the Cauchy and Piola–Kirchhoff tensors are identical. ...P}</math> is one possible solution to this problem. It defines a family of tensors, which describe the configuration of the body in either the current or the ...4 KB (594 words) - 18:36, 28 November 2024
- * The [[Symmetric tensor#Symmetric product|symmetric product]] of tensors ...452 bytes (59 words) - 21:18, 28 March 2018
- ...of tensors. It is an operation that generalizes the idea of aggregation of tensors in higher-dimensional spaces. The term "tensotory" is a neologism coined to Given a sequence of tensors <math>T_1, T_2, \dots, T_n</math>, the tensotory is defined as the iterated ...4 KB (635 words) - 01:52, 9 January 2025
- ...] [[curvature]] or harmonic [[Weyl tensor]]. In fact, existence of Codazzi tensors impose strict conditions on the [[Riemann curvature tensor|curvature tensor [[Category:Tensors]] ...3 KB (512 words) - 11:05, 3 September 2024
- [[Category:Tensors]] ...3 KB (387 words) - 18:58, 2 September 2023
- ...ectors can be symmetric, and in fact the space of symmetric <math>k</math>-tensors on a [[vector space]] <math>V</math> is [[isomorphic]] to the space of [[ho {{Tensors}} ...5 KB (762 words) - 02:02, 18 December 2023
- | title = Tensors, Differential Forms, and Variational Principles [[Category:Tensors]] ...4 KB (590 words) - 09:33, 28 November 2024
- ...to numeric requirements an explicit formulation based on a low number of [[tensors]] is desirable and was already introduced originally most explicit algebrai ...itrary tensor basis. In the present investigations an optimum set of basis tensors and the corresponding coefficients is to be found. ...7 KB (1,027 words) - 11:44, 5 August 2024
- ...is that of the [[antisymmetric tensor]] or [[alternating form]]. Symmetric tensors occur widely in [[engineering]], [[physics]] and [[mathematics]]. The space of all symmetric tensors of order ''k'' defined on ''V'' is often denoted by ''S''<sup>''k''</sup>(' ...11 KB (1,713 words) - 10:27, 10 February 2025
- [[Category:Metric tensors]] ...1 KB (155 words) - 07:14, 19 April 2024
- For ''tensors'', an appropriate generalization is needed. The proper definition for a rep ...nction (mathematics)#Restrictions and extensions|restrictions]] of spatial tensors: ...9 KB (1,360 words) - 23:07, 4 February 2025
- * [[Component-free treatment of tensors]] ...4 KB (507 words) - 21:56, 1 January 2024
- ...order-<math>M</math> tensors and the vector space of order-<math>L</math> tensors. [[Category:Tensors]] ...10 KB (1,662 words) - 23:33, 24 March 2024
- {{short description|Basis used to express spherical tensors}} ...is (linear algebra)|basis]] used to express '''[[Tensor operator|spherical tensors]]'''.{{definition needed|date=April 2020}} The spherical basis closely rel ...10 KB (1,524 words) - 07:21, 26 July 2024
- ...ock |first1=David |last2=Rund |first2=Hanno |authorlink2=Hanno Rund |title=Tensors, Differential Forms, and Variational Principles |date=1 April 1989 | publis [[Category:Tensors]] ...7 KB (1,125 words) - 16:33, 9 May 2023
- 2 KB (227 words) - 23:27, 23 January 2025
- ...ector|vectors]], and second-order [[tensor]]s with respect to second-order tensors are of considerable use in [[continuum mechanics]]. These derivatives are u == Derivatives with respect to vectors and second-order tensors == ...44 KB (6,662 words) - 04:06, 18 April 2024
- where <math>R,\overline{R}</math> are Riemann curvature tensors of <math>M,N</math>.</blockquote>In words, it states that <math>f</math> is '''Theorem''': For Riemann curvature tensors <math>R,\overline{R}</math> and all broken geodesics (a broken geodesic is ...8 KB (1,259 words) - 01:54, 10 February 2025