Concept
Separable space
Related lectures (35)
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Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Introduction: Course syllabus
Introduces the course syllabus, grading scheme, and classical and quantum computation models.
Hilbert Space: Geometry, Bases
Explores Hilbert space, scalar product, geometry, bases, complex functions, and quantum mechanics applications.
Linear Binary Classification: Perceptron, SGD, Fisher's LDA
Covers the Perceptron model, SGD, and Fisher's Linear Discriminant in binary classification.
Open Mapping Theorem
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Redescription SVM and Hilbert Spaces
Explores redescription SVM and Hilbert spaces for solving nonlinear problems using inner product spaces and separable Hilbert spaces.
Optimal Transport: Disintegration Theorem
Covers the Disintegration Theorem in the context of Optimal Transport.
Sobolev Spaces in Higher Dimensions
Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.
Graph Traversal: BFS and DFS
Covers Breadth-First Search, Depth-First Search, and topological sort in graphs.
Preimages in a Gluing Construction
Delves into preimages of closed sets in a disjoint union.