Lectures related to Discontinuous linear map

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Covers the definitions and properties of dual spaces and linear operators.

Functional Analysis and Distribution Theory

Explores different notions of function equality, linear functionals, operations on distributions, and the advantages of working with Schwartz' space.

Operator Product Expansion

Explores Operator Product Expansion (OPE) and its role in Conformal Bootstrap.

Linear Maps and Matrices

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Linear Algebra: Basis Change and Matrices

Explores basis change in linear algebra and the role of matrices.

Properties of Complete Spaces

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

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Tensor Products and Symmetric Power

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Dot Product: Properties and Applications

Explores the properties and applications of the dot product in vector spaces.

Introduction to Electronics

Delves into the practical applications of electronics in modern technology.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Linear Applications: Properties and Examples

Explores properties of linear applications, including symmetric matrices and linearity in analysis.

Objective function, Linearity and nonlinearity

Explores linear and non-linear functions in optimization, emphasizing their distinct characteristics and implications in solving problems.

Functional Analysis I: Operator Definitions

Introduces linear and bounded operators, compact operators, and the Banach space.

Kernel, Image and Linear Maps

Explains kernel, image, and linear maps, illustrating concepts with examples.

Resolving Operators: Closedness and Injectivity

Discusses resolving operators' closedness and injectivity in Banach spaces.

Quantum Field Theory: Exo Session 4

Covers exercises on Schur's lemma and the Jacobi identity in Quantum Field Theory.