Mathematics

Advanced Topics of Applied Linear Algebra Research
Editor: Niranjan Bora, PhD

Advanced Topics of Applied Linear Algebra Research

In Production
Pub Date: Forthcoming February 2027
Hardback Price: $180 USD | £140 UK
Hard ISBN: 9781779646712
E-Book ISBN: 978-1-77964-672-9
Pages: Est. 302 pp w index
Binding Type: Hardback / ebook
Notes: 17 color and 29 b/w illustrations

Linear algebra, the language of vectors, matrices, and transformations, has become a cornerstone of scientific discovery and technological advancement. Its elegance and power lie in its ability to model a vast array of phenomena, from the motion of planets to the flow of information in computer networks. The landscape of applied linear algebra research is constantly evolving, driven by the ever-growing demands of diverse scientific and technical fields. This new book, Advanced Topics of Applied Linear Algebra Research, delves into the cutting-edge research advancements that are pushing the boundaries of this vital mathematical discipline. It also bridges the gap between theoretical ideas and practical applications of linear algebra.

This book focuses on the latest applications of linear algebra research, presenting chapters from researchers from all over the globe. Chapters discuss emerging topics in matrix analysis, matrix approaches of graph theory, differential matrix equations, generalization of the second Zagreb matrix, multiparameter eigenvalue problems, fuzzy eigenvalue problem, polynomial eigenvalue problem, linear algebra in machine learning, matrices and manifolds in control theory, image compression based on singular value decomposition, channel coding problem for 6G technology, as well as linear algebra through pedagogical approaches. It demonstrates how these concepts are used in various fields such as engineering, computer science, physics, machine learning, data science, etc.

With each chapter meticulously developing the theoretical underpinnings of these advanced topics, complemented by illustrative examples and real-world applications, this book offers a practical approach that makes it relevant and valuable for readers and professionals in mathematics, computer science, engineering, physics, and other quantitative fields.

CONTENTS:
Preface

1. On Vertex Energy of a Graph and Its Extension
Erashikha Devi and Jibonjyoti Buragohain

2. Graph Theory and Matrix Approach in Applied Science
Mehboob Ali Kanhio, Zain-Ul-Abdin Khuro, and Farhat Naureen Memon

3. Matrix Properties Associated with Moran Eigenvector Maps and Eigenvector Spatial Filtering: Graph Adjacency Matrices in Practice
Daniel A. Griffith

4. Differential Matrix Equations with Singular Constant Coefficients
Ivan I. Kyrchei

5. A Generalization of the Second Zagreb Matrix
Idweep J. Gogoi, A. Mahanta, and S. Borah

6. Gerschgorin Theorem for Multiparameter Eigenvalue Problems
Songita Boruah

7. A Comprehensive Overview of Fuzzy Eigenvalue Problems and Their Applications
Mukesh Lahon

8. Polynomial Eigenvalue Problems and Their Applications
Bharati Borgohain and Ankita Kakoty

9. Linearization Method to Solve Rectangular Polynomial Two-parameter Eigenvalue Problems
Bharati Borgohain

10. A α-Spectra of Graph with Pockets
Nijara Konch and Ankur Bharali

11. Applications of Matrices and Manifolds in Control Theory
S. Priyadharsini

12. Image Compression Based on Singular Value Decomposition
Surashmi Bhattacharyya

13. Artificial Intelligence-Based Neural Network Method for a Special Class of Eigenvalue Problems
Rajdeep Bora

14. Handling Complex Topics in Linear Algebra Through Advanced Instructional Strategies
Robert Kati

15. On Topological Indices and Entropy Measures of Anticancer Drugs and Amines
Aditya Pegu and Ankur Bharali

16. On ABC Spectra of Path, Cycle, and Star Graphs
Idweep Jyoti Gogoi and Susmita Dutta

Index


About the Authors / Editors:
Editor: Niranjan Bora, PhD
Assistant Professor, Department of Mathematics, Dibrugarh University, Assam, India

Niranjan Bora, PhD, is presently working as an Assistant Professor in the Department of Mathematics at Dibrugarh University, Assam, India. Prior to this, he served as Assistant Professor in Mathematics at Dibrugarh University Institute of Engineering and Technology of Dibrugarh University. He did his MSc in Mathematics at Gauhati University, Assam, India, and PhD in Mathematics at Dibrugarh University. He has published book chapters in edited books, conference proceedings, and articles in international journals. He has actively participated in conferences and seminars, served as a guest editor of a prominent journal, and held leadership roles in professional organizations. His area of research is applied mathematics with a special focus on linear algebra. His research contributions include numerical methods, numerical linear algebra, polynomial and multiparameter eigenvalue problems, and graph theory. His goal is to take applied linear algebra to new heights by bringing together top experts and encouraging intellectual interaction.




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