Lectures related to Chaos and Lyapunov Exponents: Analyzing Predictability

Explores symmetrical bilinear forms, the Pythagorean theorem, inequalities, and orthogonal matrices.

Covers the Singular Value Decomposition (SVD) of a matrix and its applications.

Delves into Chaos Theory, exploring chaotic systems, sensitivity to initial conditions, and the dynamics of the double pendulum.

Covers Canonical Correlation Analysis, a method to find relationships between two sets of variables.

Explains the QR factorization theorem and demonstrates the Gram-Schmidt procedure with an example.

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Explores matrix decompositions for solving linear systems and simulating dynamics.

Covers the LU decomposition algorithm, transforming a matrix into L and U.