Concept

Linear form

Related lectures (31)

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

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

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

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

Explores different notions of function equality, linear functionals, operations on distributions, and the advantages of working with Schwartz' space.

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

Covers the basics of linear mapping and coordinate systems.

Covers the concept of graph sketching with a focus on connected components.

Covers distributions, linear systems, impulse response, convolution, and examples of linear systems.

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.

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

Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.

Covers the Radon-Nikodym theorem and the uniqueness of signed Borel measures.

Explores linear and non-linear functions in optimization, emphasizing their distinct characteristics and implications in solving problems.

Explores MHD equilibrium and stability, emphasizing energy considerations for determining stability.

Explores the motivation and ideas behind convolutional networks, emphasizing weight sharing and pooling layers.

Explores norms and bounded operators in functional analysis, demonstrating their properties and applications.

Explores quantum dynamics with trajectories and their applications in nonadiabatic dynamics and coupling with external fields.

Covers the solution to linear homogeneous recurrence relations with repeated roots and of arbitrary degree.