Lectures related to Finite Fields and Vector Spaces

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

Explores finite fields, vector spaces, commutative groups, and field properties, highlighting their significance in coding theory and algebraic computations.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Vector Spaces: Properties and Operations

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

Vector Spaces: Definitions and Examples

Covers vector spaces, subspaces, linear independence, and spans in finite-dimensional spaces.

Vector Spaces: Definitions and Properties

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

Matrix Operations and Vector Spaces

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

Vector Spaces: Definition, R2

Introduces vector spaces with binary addition and scalar multiplication, exploring geometric examples in R2.

Introduction to Vector Spaces

Introduces the concept of vector spaces and covers properties of vectorial subspaces.

Introduction to Finite Fields

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

Vector Subspaces

Explores the definition and properties of vector subspaces in linear algebra.

Vector Spaces: Properties and Examples

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

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 Transformation Properties

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

Vector Spaces in R2 and R3

Covers the structure of vector spaces in R2 and R3, focusing on scalar multiplication and addition.

Vector Spaces: Examples and Subspaces

Covers examples of vector spaces and the concept of subspaces, emphasizing key properties and verification methods.

Vector Spaces: Operations and Linear Transformations

Explores vector space operations, linear transformations, matrix representation, and linear applications.

Dot Product: Properties and Applications

Explores the properties and applications of the dot product in vector spaces.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.