Lectures related to Linear Systems in 2D: Stability

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Explores bistability in the cell cycle, emphasizing positive feedback mechanisms and abrupt response transformations.

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

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

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Introduces Convex Optimization notation, convex functions, vector norms, and matrix properties.

Explores eigenvalues, eigenvectors, and methods for solving linear systems with a focus on rounding errors and preconditioning matrices.

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

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.