
Abstract Algebra: Vector Spaces
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Preface
1/19/2025

Introduction to Vector Spaces
1/19/2025

Definition and Examples
1/19/2025

Subspaces
1/19/2025

Span and Linear Independence
1/19/2025

Quotient Spaces
1/19/2025

Direct Sums
1/19/2025

Vector Space Homomorphisms
1/19/2025

Dual Spaces
1/19/2025

Basis and Dimension
1/19/2025

Basis of a Vector Space
1/19/2025

Dimension Theorem
1/19/2025

Finite and Infinite Dimensions
1/19/2025

Change of Basis
1/19/2025

Coordinate Systems
1/19/2025

Extension and Reduction of Bases
1/19/2025

Applications of Dimension
1/19/2025

Linear Transformations
1/19/2025

Kernel and Image
1/19/2025

Inner Product Spaces
1/19/2025

Orthogonality
1/19/2025

Gram-Schmidt Process
1/19/2025

Orthogonal Complements
1/19/2025

Orthonormal Bases
1/19/2025

Adjoint Operators
1/19/2025

Spectral Theorem
1/19/2025

Eigenvalues and Eigenvectors
1/19/2025

Characteristic Polynomial
1/19/2025

Diagonalization
1/19/2025

Eigenspaces
1/19/2025

The Cayley-Hamilton Theorem
1/19/2025

Jordan Canonical Form
1/19/2025

Applications in Differential Equations
1/19/2025

Spectral Decomposition
1/19/2025

Applications of Vector Spaces
1/19/2025

Differential Equations
1/19/2025

Fourier Series
1/19/2025

Quantum Mechanics
1/19/2025

Computer Graphics
1/19/2025

Coding Theory
1/19/2025

Economics and Game Theory
1/19/2025

Data Science
1/19/2025

Advanced Topics in Vector Spaces
1/19/2025

Tensor Products
1/19/2025

Exterior and Symmetric Algebras
1/19/2025

Modules over a Ring
1/19/2025

Topological Vector Spaces
1/19/2025

Normed and Banach Spaces
1/19/2025

Hilbert Spaces
1/19/2025

Representation Theory
1/19/2025