Lectures related to Convex Optimization: Notation and Matrix Norms

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: Convex Optimization

Covers essential linear algebra concepts for convex optimization, including vector norms, eigenvalue decomposition, and matrix properties.

Singular Value Decomposition: Applications and Interpretation

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Linear Algebra Review

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

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Linear Independence and Basis

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

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Linear Equations: Vectors and Matrices

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Diagonalization of Linear Transformations

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.