Lectures related to Group Theory: Recalls

Introduction to Category Theory: Adjoint Functors

Explores a concrete example of adjunction in category theory and covers natural transformations and group theory concepts.

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.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

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 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 Algebra Basics

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Kernel, Image and Linear Maps

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

Linear Transformations: Matrices and Bases

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

Vector Spaces Equivalence

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Linear Algebra: Lecture Notes

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

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.

Linear Applications of Vector Spaces

Covers linear applications between vector spaces, exploring their properties and uniqueness based on bases.

Matrix Operations: Determinants and Vector Spaces

Covers strategies for matrix operations and the concept of vector spaces.

Hermitian Forms: Definition and Properties

Explores the definition and properties of Hermitian forms in complex vector spaces.

Vector Spaces: Bases and Dimension

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Linear Algebra: Vector Subspaces and Combinations

Explores vector subspaces and linear combinations in linear algebra, focusing on the reciprocal relationship between lines, columns, and elements.

Linear Applications: Injectivity and Surjectivity

Explores injective and surjective linear applications, map composition, and matrix relationships in vector spaces.

Vectorial Spaces: Counter Examples and Proofs

Explores counter examples and proofs in vectorial spaces, emphasizing rigorous reasoning.