Lectures related to Tensor | EPFL Graph Search

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Explores the transformation of vectors and tensors, including rotations and representations in quantum physics.

Tucker Decomposition: Multilinear rank and applications in data compression

Covers the Tucker decomposition and its applications in data compression, explaining the notion of multilinear rank and the HOSVD method.

Stress Components & Transformation of Tensors

Covers stress components, tensor transformation, and invariants in continuum mechanics.

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Chemical Environments: Representations and Correlations

Explores chemical environment representations, symmetrized correlations, and machine learning applications at the atomic scale.

Tensors and Lorentz Transformations

Covers tensors, Lorentz transformations, and electrodynamics in relativistic notation.

Stereographic Projection and Metric Tensors

Explores stereographic projection and metric tensors on hyperbolic planes, emphasizing isometry and conforming models.

Linear Momentum Conservation and Stress in Continuum

Explores the conservation of linear momentum and stress in a continuum, focusing on governing equations and constitutive laws.

Deformation and Strain Tensors

Explores deformation and strain tensors, Lagrange representation, elasticity theory, and the divergence theorem.

Special and General Relativity

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Principles of Quantum Physics

Covers the principles of quantum physics, focusing on tensor product spaces and entangled vectors.

Tensor Product: Bilinear Maps

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Continuum Mechanics: Mass Conservation

Explores mass conservation in continuum mechanics, covering stress, dynamics, constitutive laws, and solid deformation.

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Differential Geometry of Surfaces

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Tensor Analysis: Coordinate Systems

Covers tensor analysis for arbitrary coordinate systems and introduces Christoffel symbols.

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.