Lectures related to Isomaphic Entue: Base Canonique and Free K-Modulus

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.

Vector Spaces: Bases and Dimension

Explains bases and dimension in vector spaces, covering generative and free families, isomorphism, and key theorems.

Linear Transformations: Isomorphism and Dimension

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

Vector Spaces: Definitions and Properties

Covers the definitions and properties of vector spaces, including axioms and examples.

Linear Algebra: Matrices and Vector Spaces

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

Matrix Operations and Vector Spaces

Covers elementary matrix operations and vector spaces, including properties and conditions for invertibility.

Linear Applications: Examples and Generalities

Covers various examples and general concepts related to linear applications in algebra.

Linear Algebra Basics

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

Linear Transformations: Matrices and Bases

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

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Vector Spaces Equivalence

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

Vector Spaces: Properties and Operations

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

Linear Transformations: Kernels and Images

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

Linear Algebra: Lecture Notes

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

Linear Independence and Bases

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

Vector Spaces: Generating Families and Isomorphisms

Discusses generating families in vector spaces and conditions for linked or free families.

Introduction to Finite Fields

Covers the basics of finite fields, including arithmetic operations and properties.

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.

Orthogonality and Characters

Explains orthogonality and characters in group representations, including equivalence classes and vector space dimensions.

Linear Operators: Boundedness and Spaces

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