Concept

Tensor (intrinsic definition)

Related lectures (31)

Spherical Tensors and Wigner-Eckart Theorem

Covers the transformation of vectors and tensors in quantum physics.

Elements of Lie Groups and Algebras

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

Vector Transformation and Tense

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

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.

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.

Special and General Relativity

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

Tensors: Motivations and Introduction

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

Tensor Decomposition: Jennrich's Theorem

Covers tensor decomposition and Jennrich's theorem, focusing on tensor rank and the uniqueness of tensor decomposition.

Tensor Products of Modules

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

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Stress Components & Transformation of Tensors

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

Tensor Analysis: Coordinate Systems

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

Indicial Notation and Tensor Components

Covers the manipulation of indicial notation and tensor components, focusing on concepts such as indical notation, free indices, contraction, and the dot product.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Twister Extract

Explores a confrontation over a stolen design and the intense storm-chasing mission.

Vectors and Tensors: Mathematical Preliminaries and Transformations

Explores mathematical preliminaries of tensors and their transformations under basis rotations.

Covariant Derivatives and Christoffel Symbols

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