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
Duration:00:03:09
Introduction to Inner Product Spaces
Duration:00:00:56
Definition and Examples
Duration:00:06:18
Basic Properties of Inner Products
Duration:00:04:07
Inner Product Spaces over Complex Numbers
Duration:00:02:16
Geometric Interpretation
Duration:00:03:18
Relation to Euclidean Spaces
Duration:00:03:41
Applications in Geometry
Duration:00:03:55
Inner Products and Norms
Duration:00:00:03
Definition of Norms
Duration:00:03:24
Cauchy-Schwarz Inequality
Duration:00:03:27
Triangle Inequality
Duration:00:03:17
Orthogonality and Norm
Duration:00:03:20
Metric Spaces
Duration:00:03:20
Applications of Norms
Duration:00:04:52
Orthogonality
Duration:00:00:03
Orthogonal Vectors and Subspaces
Duration:00:05:46
Orthogonal Projections
Duration:00:05:29
Orthogonal Basis
Duration:00:05:55
Orthogonal Diagonalization
Duration:00:03:59
Orthogonalization Methods
Duration:00:04:16
Applications of Orthogonality
Duration:00:04:27
Orthonormal Bases
Duration:00:00:03
Existence and Construction
Duration:00:05:14
Gram-Schmidt Process
Duration:00:05:25
Properties of Orthonormal Bases
Duration:00:06:58
Fourier Series and Fourier Transform
Duration:00:06:49
Applications in Signal Processing
Duration:00:07:39
Applications in Quantum Mechanics
Duration:00:08:15
Definition and Properties
Duration:00:07:26
Projection Theorem
Duration:00:05:43
Least Squares Approximation
Duration:00:05:43
Orthogonal Decomposition
Duration:00:05:05
Orthogonal Projection Matrices
Duration:00:04:17
Applications in Least Squares Problems
Duration:00:04:11
Applications in Linear Regression
Duration:00:04:03
Spectral Theory of Self-adjoint Operators
Duration:00:00:05
Self-adjoint Operators
Duration:00:03:46
Spectrum of Operators
Duration:00:03:16
Spectral Theorem
Duration:00:02:45
Diagonalization of Self-adjoint Operators
Duration:00:03:18
Applications in Differential Equations
Duration:00:03:08
Applications in Functional Analysis
Duration:00:03:21
Applications of Inner Product Spaces
Duration:00:00:04
Applications in Engineering
Duration:00:03:24
Applications in Computer Science
Duration:00:03:44
Applications in Optimization
Duration:00:03:40
Applications in Data Analysis
Duration:00:03:46
Applications in Machine Learning
Duration:00:03:37
Applications in Image Processing
Duration:00:03:44
Future Directions and Open Problems
Duration:00:04:19