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Abstract Algebra: Vector Spaces

N.B. Singh

This audiobook is narrated by a digital voice. "Abstract Algebra: Vector Spaces" is a comprehensive exploration of vector spaces within the realm of abstract algebra, offering a clear and insightful journey into foundational concepts and their...

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Preface

1/19/2025
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Introduction to Vector Spaces

1/19/2025
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Definition and Examples

1/19/2025
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Subspaces

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Span and Linear Independence

1/19/2025
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Quotient Spaces

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Direct Sums

1/19/2025
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Vector Space Homomorphisms

1/19/2025
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Dual Spaces

1/19/2025
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Basis and Dimension

1/19/2025
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Basis of a Vector Space

1/19/2025
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Dimension Theorem

1/19/2025
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Finite and Infinite Dimensions

1/19/2025
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Change of Basis

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Coordinate Systems

1/19/2025
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Extension and Reduction of Bases

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Applications of Dimension

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Linear Transformations

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Kernel and Image

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Inner Product Spaces

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Orthogonality

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Gram-Schmidt Process

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Orthogonal Complements

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Orthonormal Bases

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Adjoint Operators

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Spectral Theorem

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Eigenvalues and Eigenvectors

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Characteristic Polynomial

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Diagonalization

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Eigenspaces

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The Cayley-Hamilton Theorem

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Jordan Canonical Form

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Applications in Differential Equations

1/19/2025
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Spectral Decomposition

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Applications of Vector Spaces

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Differential Equations

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Fourier Series

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Quantum Mechanics

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Computer Graphics

1/19/2025
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Coding Theory

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Economics and Game Theory

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Data Science

1/19/2025
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Advanced Topics in Vector Spaces

1/19/2025
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Tensor Products

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Exterior and Symmetric Algebras

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Modules over a Ring

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Topological Vector Spaces

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Normed and Banach Spaces

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Hilbert Spaces

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Representation Theory

1/19/2025