Lectures related to Linear Transformations: Matrices and Bases

Linear Algebra: Lecture Notes

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

Vector Spaces: Properties and Operations

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

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: Kernel and Image

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

Orthogonality and Subspace Relations

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

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Linear Transformations: Kernels and Images

Covers kernels and images of linear transformations between vector spaces.

Linear Algebra: Abstract Concepts

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

Linear Transformations: Polynomials and Bases

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Linear Algebra: Matrices and Vector Spaces

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

Linear Algebra Basics

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

Linear Transformations: Matrices and Bases

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

Linear Applications: Kernel and Image

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

Linear Transformations: Kernels and Images

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

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.

Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Linear Independence and Bases

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

Rank Theorem: Part 2

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