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Related lectures (31)

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Optimization Basics: Linear Algebra, Analysis, Convexity

Introduces optimization basics, covering linear algebra, analysis, and convexity principles.

Orthogonal Projections: Rectors and Norms

Covers orthogonal projections, rectors, norms, and geometric observations in vector spaces.

Functional Analysis I: Norms and Bounded Operators

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

Equivalent norms: properties and proofs

Explores equivalent norms in a vector space and their continuity properties, including proofs of norm equivalence.

Signal Processing: Properties and Norms

Explores the properties and norms of discrete signals in signal processing.

Sensitivity of Solutions

Explores the sensitivity of solutions in numerical methods, including linear systems and matrix norms, with an example of deblurring images.

Normed Spaces & Reflexivity

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

Functional Analysis and Distribution Theory

Introduces functional analysis, distribution theory, topological vector spaces, and linear operators, emphasizing their importance in engineering applications.

Cauchy-Schwarz Inequality: Proof and Applications

Explores the Cauchy-Schwarz inequality, norms, and inner products in a real inner product space.

Fenchel Conjugation: Basics and Applications

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