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 diverse applications. From fundamental definitions of basis and dimension to advanced topics like quantum mechanics, coding theory, and data science, this book equips readers with a robust understanding of how vector spaces underpin various theoretical frameworks and real-world problems. With an emphasis on clarity and practical relevance, it serves as an invaluable resource for students, researchers, and enthusiasts seeking to deepen their knowledge and explore the profound connections between algebraic structures and modern applications.
Duration - 2h 45m.
Author - N.B. Singh.
Narrator - Digital Voice Mary G.
Published Date - Monday, 20 January 2025.
Copyright - © 2024 N.B. Singh ©.
Location:
United States
Description:
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 diverse applications. From fundamental definitions of basis and dimension to advanced topics like quantum mechanics, coding theory, and data science, this book equips readers with a robust understanding of how vector spaces underpin various theoretical frameworks and real-world problems. With an emphasis on clarity and practical relevance, it serves as an invaluable resource for students, researchers, and enthusiasts seeking to deepen their knowledge and explore the profound connections between algebraic structures and modern applications. Duration - 2h 45m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duration:00:01:06
Introduction to Vector Spaces
Duration:00:00:59
Definition and Examples
Duration:00:02:45
Subspaces
Duration:00:02:28
Span and Linear Independence
Duration:00:02:53
Quotient Spaces
Duration:00:02:43
Direct Sums
Duration:00:02:20
Vector Space Homomorphisms
Duration:00:02:33
Dual Spaces
Duration:00:02:34
Basis and Dimension
Duration:00:00:54
Basis of a Vector Space
Duration:00:02:45
Dimension Theorem
Duration:00:02:48
Finite and Infinite Dimensions
Duration:00:03:28
Change of Basis
Duration:00:03:17
Coordinate Systems
Duration:00:03:39
Extension and Reduction of Bases
Duration:00:03:32
Applications of Dimension
Duration:00:03:43
Linear Transformations
Duration:00:01:00
Kernel and Image
Duration:00:03:28
Inner Product Spaces
Duration:00:01:01
Orthogonality
Duration:00:03:18
Gram-Schmidt Process
Duration:00:03:13
Orthogonal Complements
Duration:00:03:14
Orthonormal Bases
Duration:00:02:48
Adjoint Operators
Duration:00:03:17
Spectral Theorem
Duration:00:03:17
Eigenvalues and Eigenvectors
Duration:00:01:11
Characteristic Polynomial
Duration:00:03:36
Diagonalization
Duration:00:03:21
Eigenspaces
Duration:00:03:29
The Cayley-Hamilton Theorem
Duration:00:03:47
Jordan Canonical Form
Duration:00:02:57
Applications in Differential Equations
Duration:00:03:21
Spectral Decomposition
Duration:00:03:26
Applications of Vector Spaces
Duration:00:01:05
Differential Equations
Duration:00:04:46
Fourier Series
Duration:00:05:20
Quantum Mechanics
Duration:00:05:37
Computer Graphics
Duration:00:04:54
Coding Theory
Duration:00:05:05
Economics and Game Theory
Duration:00:04:32
Data Science
Duration:00:05:12
Advanced Topics in Vector Spaces
Duration:00:01:10
Tensor Products
Duration:00:04:53
Exterior and Symmetric Algebras
Duration:00:05:07
Modules over a Ring
Duration:00:04:47
Topological Vector Spaces
Duration:00:03:48
Normed and Banach Spaces
Duration:00:03:10
Hilbert Spaces
Duration:00:02:34
Representation Theory
Duration:00:02:43