Linear Algebra: Determinants and Eigenvalues
N.B. Singh
This audiobook is narrated by a digital voice.
Linear Algebra: Determinants and Eigenvalues is a comprehensive guide designed for absolute beginners, offering a clear and detailed introduction to the fundamental concepts of linear algebra. Focusing on determinants and eigenvalues, the book explores their definitions, properties, and practical applications. Through step-by-step explanations, numerous examples, and practical exercises, readers will build a solid foundation in these essential topics. This book is ideal for students and enthusiasts eager to understand the basics of linear algebra and its significance in various fields such as engineering, physics, computer science, and economics.
Duration - 3h 37m.
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: Determinants and Eigenvalues is a comprehensive guide designed for absolute beginners, offering a clear and detailed introduction to the fundamental concepts of linear algebra. Focusing on determinants and eigenvalues, the book explores their definitions, properties, and practical applications. Through step-by-step explanations, numerous examples, and practical exercises, readers will build a solid foundation in these essential topics. This book is ideal for students and enthusiasts eager to understand the basics of linear algebra and its significance in various fields such as engineering, physics, computer science, and economics. Duration - 3h 37m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duration:00:02:15
Introduction to Determinants
Duration:00:01:16
Definition of Determinant
Duration:00:04:10
2x2 and 3x3 Determinants
Duration:00:04:44
Properties of Determinants
Duration:00:05:24
Expansion Methods
Duration:00:05:25
Cramer’s Rule
Duration:00:04:27
Volume and Area Interpretations
Duration:00:06:09
Applications in Geometry
Duration:00:08:11
Determinants of Special Matrices
Duration:00:08:34
Multiplicative Property
Duration:00:09:18
Transpose and Inverse
Duration:00:06:18
Determinants and Eigenvalues
Duration:00:04:54
Applications in Linear Systems
Duration:00:05:28
Applications in Change of Variables
Duration:00:03:57
Computational Aspects
Duration:00:04:06
Calculation Methods for Determinants
Duration:00:01:15
Expansion by Cofactors
Duration:00:03:43
Row Reduction and Determinants
Duration:00:03:28
Block Matrices and Determinants
Duration:00:03:47
Eigenvalue Approach to Determinants
Duration:00:03:23
Determinantal Identities
Duration:00:03:59
Applications in Matrix Theory
Duration:00:04:30
Applications in Differential Equations
Duration:00:04:34
Applications of Determinants
Duration:00:01:09
Area and Volume Calculations
Duration:00:04:24
Orientation and Orientation Preserving Maps
Duration:00:04:17
Cramer’s Rule and Linear Systems
Duration:00:02:58
Determinants in Physics
Duration:00:03:39
Determinants in Economics
Duration:00:03:31
Determinants in Computer Graphics
Duration:00:04:09
Determinants in Circuit Analysis
Duration:00:04:18
Introduction to Eigenvalues
Duration:00:01:09
Definition of Eigenvalues and Eigenvectors
Duration:00:04:29
Characteristic Polynomial
Duration:00:02:58
Eigenvalues of Special Matrices
Duration:00:03:52
Geometric Interpretation
Duration:00:02:46
Algebraic and Geometric Multiplicity
Duration:00:03:09
Eigenvalue Decomposition
Duration:00:03:13
Properties of Eigenvalues and Eigenvectors
Duration:00:01:17
Diagonalizability
Duration:00:03:14
Spectral Theorem
Duration:00:04:09
Eigenvalues in Matrix Powers
Duration:00:04:15
Principal Component Analysis (PCA)
Duration:00:03:53
Jordan Canonical Form
Duration:00:03:12
Computational Aspects of Eigenvectors
Duration:00:03:23
Applications in Quantum Mechanics
Duration:00:03:43
Applications of Eigenvalues and Eigenvectors
Duration:00:01:13
Eigenvalues in Stability Analysis
Duration:00:03:01
Eigenvalues in Markov Chains
Duration:00:02:42
Eigenvalues in Google’s PageRank Algorithm
Duration:00:03:05
Eigenvalues in Vibrations and Oscillations
Duration:00:03:26
Eigenvalues in Graph Theory
Duration:00:03:16
Applications in Control Theory
Duration:00:03:14
Future Directions and Open Problems
Duration:00:03:48