PCA: Principal Components Analysis

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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.