Lectures related to Linear Maps and Bases: The Rank Theorem

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 Algebra Basics

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Linear Transformations: Matrices and Bases

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

Kernel, Image and Linear Maps

Explains kernel, image, and linear maps, illustrating concepts with examples.

Linear Transformations: Isomorphism and Dimension

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

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Linear Algebra: Lecture Notes

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

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Maps and Matrices

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Linear Transformations: Kernel and Image

Covers the concepts of kernel and image of a linear transformation and their relationship with the rank of the matrix.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Orthogonality and Subspace Relations

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

Linear Applications: Properties and Examples

Explores properties of linear applications, including symmetric matrices and linearity in analysis.

Rank Theorem: Part 2

Delves into the Rank Theorem's implications for linear transformations and mappings.

Linear Transformations: Kernels and Images

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

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces.

Linear Algebra: Matrices and Vector Spaces

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

Vector Spaces and Linear Applications

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Vector Spaces: Bases and Dimension

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Vector Spaces: Linear Applications and Generators

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