Turbulence Phenomenology

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Explores eigenvalues, eigenvectors, diagonalization, and spectral theorem in linear algebra.

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Explores eigenvalues and eigenvectors of Markov chains, focusing on convergence rates and matrix properties.

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Explores algebraic and geometric multiplicities of eigenvalues in linear algebra.

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

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

Covers the key concepts of Principal Component Analysis (PCA) and its practical applications in data dimensionality reduction and feature extraction.

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Discusses the sharp transition in mixing time of a random walk.