Concept

Seminorm

Related lectures (16)

Functional Analysis I: December 16, 2021

Explores digital integration, uniform bounds, weak convergence, and norm homogeneity in functional analysis.

Dynamics of Singular Riemann Surface Foliations

Explores the dynamics of singular Riemann surface foliations on compact Kähler manifolds.

Norms and Valuations on Fields

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Mathematics of Data: Optimization Basics

Covers basics on optimization, including norms, Lipschitz continuity, and convexity concepts.

Vector Spaces and Scalar Products

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Functional Spaces: Linear Applications

Explores functional spaces, linear applications, sublinear functionals, and the Hahn-Banach theorem.

Truncated CG: Conjugate Gradients

Covers the truncated conjugate gradients algorithm for solving positive definite linear maps iteratively.

Functional Analysis I

Covers sublinear functionals, linear functionals extension, and Hahn-Banach theorem.

Bolzano-Weierstrass Theorem: Sequential Compactness in Hilbert Spaces

Explores the Bolzano-Weierstrass theorem in Hilbert spaces, showcasing sequential compactness and the construction of converging subsequences.

Other regularizations + the Lasso

Explores diverse regularization approaches, including the L0 quasi-norm and the Lasso method, discussing variable selection and efficient algorithms for optimization.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Variational Formulation: Weak Formulations & Galerkin

Explores weak formulations, Galerkin method, and variational formulations in finite element methods.

Classification of Quadratic Forms

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

Aggregate Risk: Coherent Risk Measures

Explores the importance of aggregate risk and coherent risk measures, including their interpretation and implications.

Symmetric Matrices and Quadratic Forms

Explores symmetric matrices, quadratic forms, and critical points in functions of two variables.

Linear systems resolution

Covers the resolution of linear systems and its link to optimization problems.