Canonical Equations and Integrable Systems

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Matrix Reduction: Part 1

Covers the reduction of a linear transformation in a 2-dimensional space to find a simpler matrix representation.

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Diagonalization of Linear Maps

Explores the diagonalization of linear maps by finding a basis formed by eigenvectors.

Diagonalization of Symmetric Matrices

Covers the diagonalization of symmetric matrices, the spectral theorem, and the use of spectral decomposition.

Eigenvalues and Eigenvectors: Understanding Matrix Transformations

Explores eigenvalues and eigenvectors in matrix transformations, essential for understanding mathematical and real-world systems.

Eigenvalues and Eigenvectors: Understanding Matrix Properties

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

Canonical Transformations in Hamiltonian Formalism

Explores canonical transformations in Hamiltonian formalism, emphasizing preservation of the action principle and structure necessary for transformations.

Eigenvalues and Fibonacci Sequence

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

Diagonalization in Symmetric Matrices

Explores diagonalization in symmetric matrices, emphasizing orthogonality and orthonormal bases.