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Everything about Cartesian tensor
Representation of a tensor in Euclidean space
In geometry and linear algebra, a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from one such basis to another is done through an orthogonal transformation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Cartesian tensorA 5-minute orientation
- Skim a recent paper: Learned Tensor Low-CP-Rank and Bloch Response Manifold Priors for Non-Cartesian MRF ReconstructionInfluential work since 2022
- Pick up a classic book: Vector analysis and Cartesian tensorsThe most-reprinted book on the subject
- Read the landmark paper: Invariants of the Third-Rank Cartesian Tensor: Optical Nonlinear SusceptibilitiesCited 166 times
- Go sideways: DelA closely related topic
- Go sideways: Christoffel symbolsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
- Cartesian basis and related terminology
- Transformations of Cartesian vectors (any number of dimensions)
- Transformation of the dot and cross products (three dimensions only)
- Transformations of Cartesian tensors (any number of dimensions)
- Pseudovectors as antisymmetric second order tensors
- Vector and tensor calculus
- Difference from the standard tensor calculus
- History
🏆 Landmark papers (most cited)
Invariants of the Third-Rank Cartesian Tensor: Optical Nonlinear Susceptibilities
Cartesian Tensor Scalar Product and Spherical Harmonic Expansions in Boltzmann's Equation
Analysis of the Cartesian Tensor Transfer Method for Calculating Vibrational Spectra of Polypeptides
E(n)-Equivariant cartesian tensor message passing interatomic potential
Precise calculation of the local pressure tensor in Cartesian and spherical coordinates in LAMMPS
CARTESIAN TENSOR EXPANSION OF THE FOKKER–PLANCK EQUATION
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
A cartesian-tensor solution of the Brinkman equation
🆕 Influential since 2022
Learned Tensor Low-CP-Rank and Bloch Response Manifold Priors for Non-Cartesian MRF Reconstruction
Sombor Index over the Tensor and Cartesian Products of Monogenic Semigroup Graphs
Low-Rank Tensor Subspace Decomposition With Weighted Group Sparsity for the Acceleration of Non-Cartesian Dynamic MRI
Irreducible Cartesian tensor decomposition: A computational approach
Calibrationless multi‐slice Cartesian MRI via orthogonally alternating phase encoding direction and joint low‐rank tensor completion
📚 Books worth reading
Vector analysis and Cartesian tensorsDonald Edward Bourne · 1977
Vector analysis and cartesian tensorsD. E. Bourne · 1977- 📕Vector Analysis and Cartesian Tensors, Third EditionP. C. Kendall · 2017
- 📕Cartesian tensorsHarold Jeffreys · 1931
- 📕Cartesian tensorsJeffreys, Harold Sir. · 1931
Cartesian tensors,Harold Jeffreys · 1931
Cartesian tensorsG. Temple · 1960- 📕Irreducible Cartesian TensorsRobert F. Snider · 2017
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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