Lectures related to Linear Applications: Definitions and Properties

Linear Algebra: Rank Theorem

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

Linear Transformations: Matrices and Bases

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

Orthogonality and Subspace Relations

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

Linear Applications: Injectivity and Surjectivity

Explores injective and surjective linear applications, map composition, and matrix relationships in vector spaces.

Linear Applications: Kernel

Introduces the kernel of a linear application and its properties.

Linear Applications and Matrices

Delves into the bijection between linear applications and matrices, exploring linearity, injectivity, surjectivity, and the consequences of this relationship.

Linear Algebra: Lecture Notes

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

Linear Algebra: Subspaces and Transformations

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

Linear Applications in Vector Spaces

Discusses linear applications between vector spaces and properties of endomorphisms and automorphisms.

Vector Spaces: Properties and Operations

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

Linear Maps and Bases: The Rank Theorem

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

Vector Spaces: Linear Applications and Generators

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

Kernel, Image and Linear Maps

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

Linear Transformations: Kernels and Images

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

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.

Linear Transformations: Isomorphism and Dimension

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

Linear Transformations: Injective and Surjective

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

Linear Applications and Span

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

Linear Applications: Vector Spaces and Subspaces

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