Hamilton Formalism: Normal Coordinates

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Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

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

Covers the l2-embeddability theorem, isometric embeddings, positive semidefinite matrices, and eigenvalues computation.

Explores symmetric matrices, their diagonalization, and properties like eigenvalues and eigenvectors.

Explores the diagonalizability of symmetric matrices and their eigenvectors in an orthonormal basis.

Explores the Spectral Theorem, emphasizing the Min-Max Criterion for symmetric matrices and the properties of positive definite matrices.

Covers the basics of Conformal Field Theory, including operators and correlators.

Explores Hamiltonian mechanics, conservation laws, potential functions, and canonical transformations in analytical detail.

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

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.