Tensors: Motivations and Introduction

Related lectures (49)

Covers matrix rank, determinant, and decomposition in linear algebra.

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

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Covers the multivariate normal distribution, properties, and sampling methods.

Covers the transformation of vectors and tensors in quantum physics.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Covers tensors, loss functions, autograd, and convolutional layers in deep learning.

Covers the norm of a matrix, operator, singular values, and unitary matrices in linear algebra.

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

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

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

Covers the representations of SU(2) and their transformations in quantum mechanics.

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

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

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

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

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

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

Covers linear independence, bases, and coordinate systems with examples and theorems.

Discusses tensor transformations and diagonalization of symmetric tensors, focusing on stress analysis and the significance of principal stresses.

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