Vectors and Tensors: Mathematical Preliminaries and Spectral Decomposition

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Explores spectral and singular value decompositions of matrices.

Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

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

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.

Explores eigenvalue problems, eigenbasis, spectral theorem, and properties of normal operators.

Explores the spectral decomposition of symmetric matrices, including diagonalization and orthogonal basis change matrices.

Explores the fundamental theorem on singular values and the formation of orthonormal bases from eigenvectors.

Explores spectral clustering theory, eigenvalue decomposition, Laplacian matrix, and practical applications in identifying clusters.

Explores canonical equations, integrable systems, trajectories, and the symplectic matrix in understanding system dynamics.