Metric Spaces: Norms and Distances

Related lectures (30)

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Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

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

Explores orthogonality, triangle inequality, and the Pythagorean theorem in vector spaces.

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

Covers the definition of norm, distance between vectors, and Cauchy-Schwarz inequality.

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

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

Covers normed vector spaces, topology in R^n, and the principle of drawers as a demonstration method.

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.