Lectures related to Linear Transformations: Isomorphism and Dimension

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 Transformations: Kernels and Images

Covers kernels and images of linear transformations between 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.

Linear Algebra: Lecture Notes

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

Vector Spaces: Linear Applications and Generators

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

Linear Applications and Span

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

Rank Theorem: Part 2

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

Vector Spaces: Definitions and Examples

Covers the definition and examples of vector spaces, including subspaces and linear transformations.

Linear Maps and Bases: The Rank Theorem

Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.

Linear Algebra: Matrices and Vector Spaces

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

Orthogonality and Subspace Relations

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

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 Applications: Examples and Generalities

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

Linear Applications Overview

Explores linear applications, vector spaces, kernels, and invertibility in linear algebra.

Linear Algebra: Change of Basis and Matrix Representation

Explores changing bases in vector spaces and matrix representation of linear transformations.

Linear Applications: Kernel and Image

Covers the concepts of kernel and image of a linear application in linear algebra.

Linear Algebra Basics

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

Kernel, Image and Linear Maps

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

Matrix Dimension Calculation

Explains how to calculate the dimension of a kernel of a matrix transpose.