Endomorphisms: Matrix Equivalence

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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.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Categorical Perspective: Group Actions

Generalizes group actions beyond sets, providing a comprehensive framework for various mathematical contexts.

Linear Applications and Span

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

Linear Transformations: Isomorphism and Dimension

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

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: Vector Spaces & Operators

Explores vector spaces, linear transformations, matrices, eigenvalues, inner products, and operators.

Linear Applications in Vector Spaces

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

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Advanced Linear Algebra: Matrices Conjugation and Equivalence

Explores matrices conjugation, equivalence, and similarity in advanced linear algebra.