etc. AND a tensor usually has all values linked somehow, so the tensor obeys transformation rules such as being able to be rotated or scaled. Examples: • in physics a tensor can show the amount and direction of stress throughout an object • in machine learning a tensor can show the values at nodes in a neural networkDonate...
Journal of the Mechanics and Physics of SolidsLi, X.S., Dafalias, Y.F., 2015. Dissipation consistent fabric tensor definition from DEM to continuum for granular media. J. Mech. Phys. Solids 78, 141-153.Li, X.S., Dafalias, Y.F.: Dissipation consistent fabric tensor defi- nition from ...
Definition 1.2.2 (ℓp-norm [6]) For matrix A∈RI×J, its ℓp-norm is defined as (1.1)‖A‖p=(∑i=1I∑j=1Jai,jp)1/p. Definition 1.2.3 (Matrix nuclear norm [7]) The nuclear norm of matrix A is denoted as ‖A‖⁎=∑iσi(A), where σi(A) is the i-th largest...
(seeCartesian coordinates). Tensors appear throughout mathematics, though they were first treated systematically in thecalculusof differential forms and indifferential geometry. They play an important role in mathematical physics, particularly in the theory ofrelativity. Tensors are also important in the...
(12) where is the pullback map of a form is defined using the transpose of the Jacobian. This definition can be extended similarly to other tensor products of and . When there is a change of coordinates, then tensors transform similarly, with the Jacobian of the linear transformation. See...
In the spirit of keeping a hot thread going, here's another possibly provocative suggestion: there is no such thing as "a tensor". That would certainly make life easier. I.e. "tensor" is a verb, not a noun. That would be a re-definition/different use of the term "tensor". Ev...
IN IRREDUCIBLE TENSOR PRODUCTSRelation Valid for Commuting as well as Non-Commuting TensorsRelations for Commuting TensorsRelatlons for Non-Commuting Tensors#DEFINITION AND PROPERTIES OF IRREDUCIBLE TENSORSDefinitionCovariant and Contravariant ComponentsTransformation of Irreducible Tensors Under a Rotation of...
(Arute et al.2019). Notably, the convergence of these disciplines can result in synergistic improvements and new views on a wide range of difficult challenges (Xiao et al.2022). Combining physics principles and classical machine learning approaches has shown significant promise in tackling quantum ...
Given this definition, a HaPPY code is then defined as a tensor network of perfect tensors over a hyperbolic tiling, such that contraction over the physical indices between adjacent tiles/tensors results in an isometry from the bulk degrees of freedom to the physical degrees of freedom on the...
Physics[TensorArray] - construct an Array that can be indexed to return the values of a tensorial expression Calling Sequence TensorArray(expression, ...) Parameters expression - any algebraic tensorial expression having spacetime free indices possibly..