Lectures related to Tensor Products and Symmetric Power

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Explores the construction of group representations through various methods and provides an illustrative example using the standard representation of sr2 on c2.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Linear Algebra Basics

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

Representation Theory: Algebras and Homomorphisms

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Dirac's Notation, Tensor Product

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Linear Algebra: Lecture Notes

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Lines Spaces and Equivalent Matrices

Covers the concept of lines spaces and equivalent matrices in linear algebra.

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Normed Spaces

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

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Diagonalization of Matrices and Least Squares

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

Lorentz Transformations and Covariant Tensors

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Bilinear Forms: Theory and Applications

Covers the theory and applications of bilinear forms in various mathematical contexts.

Kernel, Image and Linear Maps

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

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Algebra: Matrix Operations and Basis

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.