Lectures related to Linear Algebra: Subspaces and Transformations

Linear Algebra: Matrices and Vector Spaces

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

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

Linear Independence and Basis

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

Kernel, Image and Linear Maps

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

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Algebra: Matrix Operations and Basis

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Linear Transformations: Matrices and Applications

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Linear Algebra: Subspaces and Combinations

Explores subspaces and linear combinations in linear algebra.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Linear Combinations and Basis Characterization

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

Linear Applications: Matrices and Transformations

Covers linear applications, matrices, transformations, and the principle of superposition.

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: Polynomials and Bases

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

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Linear Algebra Basics

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

Linear Independence: Definition and Examples

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

Vector Spaces: Bases and Dimension

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

Linear Algebra Review: Vector Spaces and Matrix Operations

Offers a quick review of key linear algebra concepts essential for further topics.

Linear Transformations: Matrices and Bases

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

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.