Concept

Dual space

Related lectures (32)

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Explores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

Covers the definitions and properties of dual spaces and linear operators.

Explores the Landau approximation applied to the Ising model in statistical physics.

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Explores the concept of dual bases in linear algebra and their practical applications.

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

Covers Lagrangian, dual function, dual problem, weak duality, and optimality.

Introduces Fenchel conjugation, exploring its properties, examples, and applications in nonsmooth optimization problems and minimax formulations.

Explores the weak formulation of linear elliptic partial differential equations and the concept of weak solutions in PDEs.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers weak and strong duality in optimization problems, focusing on Lagrange multipliers and KKT conditions.

Explores flow projection on stable and unstable manifolds using dual basis and Gram-Schmidt, with practical error quantification.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Explores bases, dual spaces, and linear applications in linear algebra.

Covers differential forms, invariant measures, and integration on manifolds with examples and illustrations.

Covers dimension theorems for linear transformations, bijectivity, isomorphism, dual spaces, and canonical applications.

Covers the concept of functors, assigning morphisms and dual spaces in different categories.