Lectures related to Integration of Rational Functions

Covers the theory of harmonic response, including decomposition into simple elements and stable system behavior.

Matrix Diagonalization: Spectral Theorem

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

Unsupervised Learning: Principal Component Analysis

Covers unsupervised learning with a focus on Principal Component Analysis and the Singular Value Decomposition.

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Singular Value Decomposition

Explores Singular Value Decomposition and its role in unsupervised learning and dimensionality reduction, emphasizing its properties and applications.

Matrix Decompositions: LU, Cholesky, QR, Eigendecomposition

Explores matrix decompositions, algorithms, computational complexity, and predator-prey interactions in numerical linear algebra.

Linear Algebra Review

Covers the basics of linear algebra, including matrix operations and singular value decomposition.

Integral Techniques: Rational Functions

Explores integrating rational functions using decomposition and division techniques with step-by-step examples.