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Related lectures (31)

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Covariance: Understanding the Concepts

Explores the concept of covariance, its meanings, and practical applications in tensor transformation laws.

Physics-inspired Machine Learning for Materials Discovery

Delves into physics-inspired machine learning for materials discovery, emphasizing atomic-scale modeling, thermodynamics, anharmonic free energies, and symmetry in machine learning models.

Vectors and Tensors: Mathematical Preliminaries and Transformations

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

Mathematical Basics: Index Notation and Tensors

Covers index notation basics and introduces tensors and their transformations.

Deep Learning Building Blocks

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

Tensors: Motivations and Introduction

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

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Tensor Decomposition: Jennrich's Theorem

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

Gyroscopic Effects in Physics

Explores gyroscopic effects, moments of inertia, and conservation of angular momentum in rotating objects and the precession of the earth's axis.

Power Method and Applications

Explores the power method and its applications in topic models and document analysis, emphasizing iterative processes and probability distribution reconstruction.