Linear Transformations: Dimension Theorems

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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.

Normed Spaces

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Linear Transformations: Isomorphism and Dimension

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

Endomorphisms: Matrix Equivalence

Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.

Linear Forms in Vector Spaces

Covers the definition and properties of linear forms in vector spaces, including generating families and direct sums.

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.

Visualizing Fourth Dimension

Explores visualizing the Fourth Dimension and introduces vector spaces, linear applications, and transformations.

Linear Algebra: Lecture Notes

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

Matrix Dimension Calculation

Explains how to calculate the dimension of a kernel of a matrix transpose.