Canonical Equations and Integrable Systems

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Related lectures (29)

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Canonical Equations: Solutions and Impulses

Explores canonical equations for isolated systems, finding solutions and analyzing impulses.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Canonical Transformations: Properties and Applications

Explores canonical transformations, their properties, and applications in Hamiltonian mechanics, emphasizing their role in simplifying the analysis of complex systems.

Eigenvalues and Eigenvectors in 3D

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Diagonalization of Linear Transformations

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Calcul de valeurs propres

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

Matrix Diagonalization: Spectral Theorem

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

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.