Lectures related to Linear Applications in 3D: Rank Theorem

Linear Transformations: Matrices and Applications

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

Linear Transformations: Matrices and Bases

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

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

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: Rank Theorem

Covers the Rank Theorem in linear algebra, focusing on vector spaces and linear applications.

Linear Algebra: Systems and Subspaces

Covers linear systems, vector subspaces, and the kernel and image of linear applications.

Linear Applications: Kernel

Introduces the kernel of a linear application and its properties.

Vector Spaces and Linear Applications

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

Linear Applications: Definitions and Matrices

Covers the definition of linear applications in IR³ to R³ and explores examples and properties.

Linear Applications: Vector Spaces and Subspaces

Explores linear applications in vector spaces, emphasizing subspaces and properties of linear maps.

Linear Algebra: Rank Theorem

Explores the Rank Theorem in linear algebra, covering matrix properties and determinants.

Linear Algebra: Image and Kernel Revisited

Revisits bases of the image and kernel in linear algebra, focusing on linear transformations between finite-dimensional vector spaces.

Linear Applications: Properties and Examples

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

Orthogonality and Subspace Relations

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

Linear Algebra: Applications and Bases

Explores unique solutions, linear dependence, canonical bases, and linear maps in linear algebra.

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 Algebra Basics

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

Linear Applications: Kernel and Image

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

Linear Transformations: Injective and Surjective

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Linear Applications: Matrices and Rank Theorem

Explores linear applications, matrices, ranks, kernels, and dimensions in linear algebra.