Linear Algebra: Rank Theorem

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Orthogonality and Subspace Relations

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

Linear Algebra: Lecture Notes

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

Linear Applications and Matrices

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

Linear Applications and Span

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

Kernel, Image and Linear Maps

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

Linear Applications: Injectivity and Surjectivity

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

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 Transformations: Kernels and Images

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

Linear Algebra: Systems and Subspaces

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

Linear Algebra: Vector Spaces and Applications

Covers linear dependence, independence, and applications in vector spaces.