Linear Systems in 2D: Stability

Related lectures (29)

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

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

Covers phase portraits, eigenvalue decomposition, Jordan decomposition, and stable nodes in non-linear systems.

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Explores phase portraits in 2D systems and the dynamics of predator-prey models.

Covers linear systems in continuous time, stability analysis, and mass-spring system examples.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Explores the effect of rounding errors in solving linear systems using the LU factorization method.

Explores nonlinear systems through phase portraits in 2D, focusing on vector fields, isoclines, and trajectories.

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