Lectures related to Visualizing Fourth Dimension

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.

Discusses linear applications between vector spaces and properties of endomorphisms and automorphisms.

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 Transformations: Isomorphism and Dimension

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

Vector Spaces: Linear Applications and Generators

Introduces vector spaces, linear applications, generators, and dimensionality in mathematics.

Linear Transformations: Dimension Theorems

Covers dimension theorems for linear transformations, bijectivity, isomorphism, dual spaces, and canonical applications.

Linear Algebra: Matrices and Vector Spaces

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

Linear Applications: Examples and Generalities

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

Linear Transformations: Kernels and Images

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

Linear Transformations: Matrices and Bases

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

Linear Applications and Span

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

Linear Algebra: Lecture Notes

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

Linear Forms in Vector Spaces

Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces.

Linear Algebra: Matrices and Endomorphisms

Explores properties of matrices, endomorphisms, and linear applications in vector spaces.

Linear Mapping and Bases

Explores linear mapping, isomorphism, and change of bases in vector spaces.

Linear Transformations: Matrices and Bases

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

Linear Independence: Definition and Examples

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Lorentz Transformations and Covariant Tensors

Explores Lorentz transformations, covariant tensors, rotational invariance, and linear transformations in vector spaces.

Vector Spaces: Bases and Dimension

Explores vector spaces, bases, and dimensions, including properties and proofs.