Lectures related to Vector Spaces: Dimension and Generators

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

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

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 Algebra Basics

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

Linear Algebra: Abstract Concepts

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

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.

Linear Transformations: Matrices and Bases

Covers the method to calculate the images of vectors in a given base.

Visualizing the Fourth Dimension: A Mathematical Journey

Explores visualizing the Fourth Dimension through points, lines, circles, spheres, and punching through, covering vector space properties, dimensionality, bases, and theorems.

Linear Transformations: Isomorphism and Dimension

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

Linear Independence and Bases

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

Orthogonality and Characters

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

Vector Spaces: Definitions and Properties

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

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

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.

Linear Operators: Boundedness and Spaces

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

Linear Transformations: Matrices and Bases

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

Linear Algebra: Lecture Notes

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