Shape Change and Polar Decomposition

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Solid Mechanics Principles: Eigenstrains

Covers eigenstrains, deformations in a body not caused by stress, and their significance in mechanics.

Continuum Mechanics: Forces and Deformation

Covers continuum mechanics, forces transmission, energy conservation, solid deformation, and tensor calculus, emphasizing the symmetry of principle strains and the geometric interpretation of eigen vectors.

Singular Value Decomposition: Theory and Applications

Covers the theory and applications of Singular Value Decomposition in computational physics, including solving linear systems and polynomial fits.

Elastic Inclusions

Explores elastic inclusions, discussing strain and stress fields, Eshelby method, and energy storage.

Matrix Diagonalization: Spectral Theorem

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.

Continuum Mechanics: Forces and Deformation

Explores the laws of dynamics, stress, energy conservation, and deformation in continuum mechanics.

Singular Value Decomposition

Explores Singular Value Decomposition and its role in unsupervised learning and dimensionality reduction, emphasizing its properties and applications.

Spectral Clustering: Finding Clusters

Explores Spectral Clustering, eigenvalue decomposition, Laplacian matrices, and cluster identification through eigenvector projections.

Canonical Correlation Analysis: Overview

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

Singular Value Decomposition

Explores Singular Value Decomposition, low-rank approximation, fundamental subspaces, and matrix norms.