Lectures related to Cauchy-Schwarz Inequality: Proof and Applications

Euclidean Norm: Properties and Special Cases

Explores the Euclidean norm properties, special cases, and applications of the Cauchy-Schwarz inequality.

Vector Spaces and Topology

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

Euclidean Norm and Triangular Inequality

Explores the Euclidean norm, triangular inequality, and distance calculations in R².

Norme, Cauchy-Schwarz Inequality

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

Real Vector Space: Basics

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

Vector Spaces and Topology

Covers vector spaces, topology, and proof methods like the pigeonhole principle in R^n.

Orthogonality and Least Squares Methods

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Metric Spaces: Norms and Distances

Explores norms, distances, scalar products, and norm convergence in metric spaces.

Orthogonality and Least Squares Method

Introduces orthogonal vectors, scalar product, Euclidean norm, Pythagorean theorem, and unit vectors.

Euclidean Spaces: Properties and Concepts

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

Normed Spaces: Definitions and Examples

Covers normed vector spaces, including definitions, properties, examples, and sets in normed spaces.

Norms in Rn

Covers the concept of norms in Rn and their applications.

Properties of Weak Derivatives

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.

Matrices and Orthogonal Transformations

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

Weak Formulation of Elliptic PDEs

Covers the weak formulation of elliptic partial differential equations and the uniqueness of solutions in Hilbert space.

Complex Functions: Norm Equivalence

Explores norm equivalence in complex functions, covering homogeneity and triangular inequality.

Standard Properties: Distance and Norm

Covers the standard properties of distance and norm in vector spaces.

Properties of Complete Spaces

Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.

Signals & Systems II: Discrete Signal Spaces

Explores discrete signal spaces, non-Euclidean norms, and the distinction between bounded and unrestricted signals.

Orthogonality and Least Squares Method

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