Metric Spaces: Norms and Distances

Related lectures (30)

Page 2 of 3

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

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

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Covers convergence, completeness, and properties of metric spaces and Banach spaces.

Explores the properties of orthonormal vectors in Euclidean space through key equations and demonstrations.

Covers the construction of Qp, norms, valuations, and Ostrovski's theorem.

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

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

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

Explores optimal transport in heat equations and metric spaces.