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
Duración:00:01:06
Introduction to Vector Spaces
Duración:00:00:59
Definition and Examples
Duración:00:02:45
Subspaces
Duración:00:02:28
Span and Linear Independence
Duración:00:02:53
Quotient Spaces
Duración:00:02:43
Direct Sums
Duración:00:02:20
Vector Space Homomorphisms
Duración:00:02:33
Dual Spaces
Duración:00:02:34
Basis and Dimension
Duración:00:00:54
Basis of a Vector Space
Duración:00:02:45
Dimension Theorem
Duración:00:02:48
Finite and Infinite Dimensions
Duración:00:03:28
Change of Basis
Duración:00:03:17
Coordinate Systems
Duración:00:03:39
Extension and Reduction of Bases
Duración:00:03:32
Applications of Dimension
Duración:00:03:43
Linear Transformations
Duración:00:01:00
Kernel and Image
Duración:00:03:28
Inner Product Spaces
Duración:00:01:01
Orthogonality
Duración:00:03:18
Gram-Schmidt Process
Duración:00:03:13
Orthogonal Complements
Duración:00:03:14
Orthonormal Bases
Duración:00:02:48
Adjoint Operators
Duración:00:03:17
Spectral Theorem
Duración:00:03:17
Eigenvalues and Eigenvectors
Duración:00:01:11
Characteristic Polynomial
Duración:00:03:36
Diagonalization
Duración:00:03:21
Eigenspaces
Duración:00:03:29
The Cayley-Hamilton Theorem
Duración:00:03:47
Jordan Canonical Form
Duración:00:02:57
Applications in Differential Equations
Duración:00:03:21
Spectral Decomposition
Duración:00:03:26
Applications of Vector Spaces
Duración:00:01:05
Differential Equations
Duración:00:04:46
Fourier Series
Duración:00:05:20
Quantum Mechanics
Duración:00:05:37
Computer Graphics
Duración:00:04:54
Coding Theory
Duración:00:05:05
Economics and Game Theory
Duración:00:04:32
Data Science
Duración:00:05:12
Advanced Topics in Vector Spaces
Duración:00:01:10
Tensor Products
Duración:00:04:53
Exterior and Symmetric Algebras
Duración:00:05:07
Modules over a Ring
Duración:00:04:47
Topological Vector Spaces
Duración:00:03:48
Normed and Banach Spaces
Duración:00:03:10
Hilbert Spaces
Duración:00:02:34
Representation Theory
Duración:00:02:43