Lectures related to PCA: Principal Components Analysis

Convex Optimization: Notation and Matrix Norms

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

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Optimal Decision Making: The Simplex Method

Introduces the Simplex Method for optimal decision making in linear programming, covering basic and advanced concepts.

Kernel PCA: Nonlinear Dimensionality Reduction

Explores Kernel Principal Component Analysis, a nonlinear method using kernels for linear problem solving and dimensionality reduction.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Principal Component Analysis: Dimension Reduction

Covers Principal Component Analysis for dimension reduction in biological data, focusing on visualization and pattern identification.

Matrix Dimension Calculation

Explains how to calculate the dimension of a kernel of a matrix transpose.

Matrix Rank and Linear Systems

Explores matrix rank, subspaces, and their role in solving linear systems of equations.

QED: Gauge Theories

Covers Quantum Electrodynamics (QED), instantons, Feynman rules, and gauge theories in modern particle physics.

Linear Systems: Continuous Time

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

Matrix Operations: Transposition, Rank, and Basis Change

Covers matrix transposition, rank, and basis change in linear algebra, exploring invertibility criteria and basis relationships.

Introduction to Quantum Mechanics

Introduces quantum mechanics, covering S-matrix, scattering amplitudes, and optical theorem.

Convex Optimization: Linear Algebra Review

Provides a review of linear algebra concepts crucial for convex optimization, covering topics such as vector norms, eigenvalues, and positive semidefinite matrices.

Linear Algebra Review

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

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Matrices: Elementary Linear Algebra

Explores elementary linear algebra concepts related to matrices, including invertible connections and matrix rank.

Diagonalization in 3D Linear Algebra

Explores diagonalization in 3D linear algebra, covering conditions for diagonalizability and eigenvectors.

Singular Value Decomposition: Applications and Interpretation

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

Structure of Algebras

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Matrix Rank: Row-Column Rank Relationship

Explores the relationship between row and column ranks of matrices and the concept of linearly independent vectors.