Metrics: Line and Convex Cone

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Introduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.

Linear Independence and Basis

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

Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Vector Calculus in 3D

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Principal Component Analysis: Dimensionality Reduction

Covers Principal Component Analysis for dimensionality reduction, exploring its applications, limitations, and importance of choosing the right components.

Convex Optimization: Convex Functions Log in to Mediaspace to watch this video

Covers the concept of convex functions and their applications in optimization problems.

Optimal Transport: Rockafellar Theorem Log in to Mediaspace to watch this video

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Convex Optimization: Elementary Results Log in to Mediaspace to watch this video

Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.

Farkas' Lemma: Applications in Game Theory Log in to Mediaspace to watch this video

Explores Farkas' Lemma, hyperplane separation, combinatorics, and its application in game theory, focusing on penalty kick strategies.

Geodesic Convexity: Theory and Applications Log in to Mediaspace to watch this video

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Linear Algebra: Matrices and Vector Spaces Log in to Mediaspace to watch this video

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Linear Algebra: Linear Dependence and Independence Log in to Mediaspace to watch this video

Explores linear dependence and independence of vectors in geometric spaces.

Linear Algebra: Systems of Equations and Vector Operations Log in to Mediaspace to watch this video

Explores systems of equations, vector operations, and geometric interpretations in linear algebra.

Linear Combinations: Vectors and Matrices Log in to Mediaspace to watch this video

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Matrix Operations: Linear Systems and Solutions Log in to Mediaspace to watch this video

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

Convexity: Functions and Global Minima Log in to Mediaspace to watch this video

Explores convex functions, global minima, and their relationship with differentiability.

Linear Independence in Vector Spaces Log in to Mediaspace to watch this video

Explores linear independence in vector spaces and the concept of bases.

Convex Sets: MGT-418 Lecture Log in to Mediaspace to watch this video

On Convex Optimization covers course organization, mathematical optimization problems, solution concepts, and optimization methods.

Vector Spaces: Properties and Operations Log in to Mediaspace to watch this video

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Linear Equations: Vectors and Matrices Log in to Mediaspace to watch this video

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

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