Linear Transformations: Isomorphism and Dimension

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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.