Linear Algebra: Inner Product Spaces
N.B. Singh
This audiobook is narrated by a digital voice.
"Linear Algebra: Inner Product Spaces" is a comprehensive introductory guide designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra within the context of inner product spaces. This book provides clear explanations and practical examples to facilitate understanding of vectors, matrices, orthogonality, projections, and their applications across diverse fields such as quantum mechanics, signal processing, and machine learning. With an emphasis on accessibility and relevance, it equips readers with essential tools to comprehend and apply linear algebra in solving real-world problems and advancing their mathematical proficiency.
Duration - 3h 38m.
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. "Linear Algebra: Inner Product Spaces" is a comprehensive introductory guide designed for absolute beginners seeking to grasp the fundamental concepts of linear algebra within the context of inner product spaces. This book provides clear explanations and practical examples to facilitate understanding of vectors, matrices, orthogonality, projections, and their applications across diverse fields such as quantum mechanics, signal processing, and machine learning. With an emphasis on accessibility and relevance, it equips readers with essential tools to comprehend and apply linear algebra in solving real-world problems and advancing their mathematical proficiency. Duration - 3h 38m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duración:00:03:09
Introduction to Inner Product Spaces
Duración:00:00:56
Definition and Examples
Duración:00:06:18
Basic Properties of Inner Products
Duración:00:04:07
Inner Product Spaces over Complex Numbers
Duración:00:02:16
Geometric Interpretation
Duración:00:03:18
Relation to Euclidean Spaces
Duración:00:03:41
Applications in Geometry
Duración:00:03:55
Inner Products and Norms
Duración:00:00:03
Definition of Norms
Duración:00:03:24
Cauchy-Schwarz Inequality
Duración:00:03:27
Triangle Inequality
Duración:00:03:17
Orthogonality and Norm
Duración:00:03:20
Metric Spaces
Duración:00:03:20
Applications of Norms
Duración:00:04:52
Orthogonality
Duración:00:00:03
Orthogonal Vectors and Subspaces
Duración:00:05:46
Orthogonal Projections
Duración:00:05:29
Orthogonal Basis
Duración:00:05:55
Orthogonal Diagonalization
Duración:00:03:59
Orthogonalization Methods
Duración:00:04:16
Applications of Orthogonality
Duración:00:04:27
Orthonormal Bases
Duración:00:00:03
Existence and Construction
Duración:00:05:14
Gram-Schmidt Process
Duración:00:05:25
Properties of Orthonormal Bases
Duración:00:06:58
Fourier Series and Fourier Transform
Duración:00:06:49
Applications in Signal Processing
Duración:00:07:39
Applications in Quantum Mechanics
Duración:00:08:15
Definition and Properties
Duración:00:07:26
Projection Theorem
Duración:00:05:43
Least Squares Approximation
Duración:00:05:43
Orthogonal Decomposition
Duración:00:05:05
Orthogonal Projection Matrices
Duración:00:04:17
Applications in Least Squares Problems
Duración:00:04:11
Applications in Linear Regression
Duración:00:04:03
Spectral Theory of Self-adjoint Operators
Duración:00:00:05
Self-adjoint Operators
Duración:00:03:46
Spectrum of Operators
Duración:00:03:16
Spectral Theorem
Duración:00:02:45
Diagonalization of Self-adjoint Operators
Duración:00:03:18
Applications in Differential Equations
Duración:00:03:08
Applications in Functional Analysis
Duración:00:03:21
Applications of Inner Product Spaces
Duración:00:00:04
Applications in Engineering
Duración:00:03:24
Applications in Computer Science
Duración:00:03:44
Applications in Optimization
Duración:00:03:40
Applications in Data Analysis
Duración:00:03:46
Applications in Machine Learning
Duración:00:03:37
Applications in Image Processing
Duración:00:03:44
Future Directions and Open Problems
Duración:00:04:19