Linear Systems in 2D: Stability

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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.