Lectures related to Permutations and Adjacency

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

Linear Transformations: Matrices and Bases

Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.

Subgroups and Cosets: Lagrange's Theorem

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Concrete Categories

Covers concrete categories with sets and structures, including Ens, Gr, Ab, and Vectk.

Linear Algebra: Matrices and Vector Spaces

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

Linear Algebra: Lecture Notes

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

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces, illustrating properties and providing proofs.

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces.

Dihedral Group: Symmetries and Cosets

Explores the symmetries of a regular n-gon, normal subgroups, cosets, and Lagrange's theorem.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Linear Applications and Span

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Lorentz Transformations and Covariant Tensors

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

Matrix Dimension Calculation

Explains how to calculate the dimension of a kernel of a matrix transpose.

Linear Algebra: Change of Basis and Matrix Representation

Explores changing bases in vector spaces and matrix representation of linear transformations.

Linear Transformations: Isomorphism and Dimension

Covers isomorphism, dimension, bases, and rank in linear transformations between vector spaces.

Linear Transformations: Matrices and Bases

Covers the method to calculate the images of vectors in a given base.

Linear Transformation Properties

Explores the properties of linear transformations through step-by-step calculations and matrix manipulations.

Endomorphisms: Matrix Equivalence

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.