Concept

Topological vector space

Related lectures (27)

Polynomials: Operations and Properties

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

Linear Algebra Basics

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

Vector Spaces: Properties and Operations

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

Linear Algebra: Lecture Notes

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

Tangent Spaces and Submersions

Covers tangent spaces and submersions in differential geometry, emphasizing vector spaces and differentiable structures.

Linear Transformations: Kernels and Images

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

Linear Independence and Bases

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

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Linear Algebra: Abstract Concepts

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

Matrix Operations: Determinants and Vector Spaces

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

Introduction to Finite Fields

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

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.

Orthogonal Complement in Rn

Covers the concept of orthogonal complement in Rn and related propositions and theorems.

Orthogonal Vectors and Projections

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Linear Operators: Boundedness and Spaces

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

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.

Vector Spaces Equivalence

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

Linear Applications of Vector Spaces

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

Linear Algebra: Matrices and Vector Spaces

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