Vector Spaces and Topology

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Related lectures (29)

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Numerical Analysis and Optimization: Concepts of Distance and Subsets

Introduces key concepts in numerical analysis and optimization, focusing on distances, subsets, and their properties in R^n.

Metric Spaces: Topology and Continuity

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

General Manifolds and Topology

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Geometric Considerations in Rn

Covers the concept of intervals in Rn using geometric balls and defines open and closed sets, interior points, boundaries, closures, bounded domains, and compact sets.

Physics 1: Vectors and Dot Product

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

Matrices and Orthogonal Transformations

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Definition of Sobolew Spaces

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Scalar Product and Euclidean Spaces

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

Real Vector Space: Basics

Introduces the basics of real vector spaces, norms, and scalar products.