Lectures related to Endomorphisms: Matrix Equivalence

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

Linear Transformations: Matrices and Bases

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

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

Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Visualizing Fourth Dimension

Explores visualizing the Fourth Dimension and introduces vector spaces, linear applications, and transformations.

Matrix Dimension Calculation

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

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces.

Linear Algebra: Matrices and Vector Spaces

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

Linear Transformations: Kernels and Images

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

Linear Transformations: Dimension Theorems

Covers dimension theorems for linear transformations, bijectivity, isomorphism, dual spaces, and canonical applications.

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 Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Linear Applications and Span

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

Linear Transformations: Isomorphism and Dimension

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

Linear Transformations: Kernel and Image

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Linear Algebra: Vector Spaces & Operators

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Linear Applications in Vector Spaces

Discusses linear applications between vector spaces and properties of endomorphisms and automorphisms.

Linear Independence and Bases

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

Advanced Linear Algebra: Matrices Conjugation and Equivalence

Explores matrices conjugation, equivalence, and similarity in advanced linear algebra.