Finite Fields and Vector Spaces

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Related lectures (28)

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Linear Algebra: Abstract Concepts

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

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Polynomials: Operations and Properties

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

Vector Spaces: Definitions and Properties

Covers the definition of vector spaces, subspaces, and linear combinations of vectors.

Vector Spaces: Definitions and Examples

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

Linear Combinations and Vector Spaces

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

Matrix Operations and Vector Spaces

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

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with 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.