Lectures related to Kernel Methods: Representer Theorem & ERM

Explores the link between linear systems and optimization through elimination and LU decomposition.

Singular Value Decomposition: Applications and Interpretation

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

Convex Optimization Tutorial: KKT Conditions

Explores KKT conditions in convex optimization, covering dual problems, logarithmic constraints, least squares, matrix functions, and suboptimality of covering ellipsoids.

Convex Optimization: Notation and Matrix Norms

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

Optimal Control: KKT Conditions

Explores optimal control and KKT conditions for non-linear optimization with constraints.

Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Matrices and Quadratic Forms: Key Concepts in Linear Algebra

Provides an overview of symmetric matrices, quadratic forms, and their applications in linear algebra and analysis.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Information Measures: Part 2

Covers information measures like entropy, joint entropy, and mutual information in information theory and data processing.

Linear Algebra: Matrices Properties

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

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Robust Optimization: Polynomial Optimization

Explores polynomial optimization, including writing polynomials as matrix products and solving linear equations for nonnegativity.

Linear Independence and Basis

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

Quadratic Forms in IR³

Explores quadratic forms in IR³, matrix properties, diagonalization, and positive definite matrices.

Dynamic Programming: Rod Cutting and Matrix Chain Multiplication

Introduces dynamic programming with a focus on rod cutting and matrix chain multiplication.

Orthogonal Linear Maps

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Matrix Operations: Composition and Product

Covers the composition and product of matrices, including matrix multiplication.

Characteristic Polynomials and Similar Matrices

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

Density Operator: Quantum Physics II

Covers the concept of matrix to the density operator in quantum physics.