Applied Linear Algebra, Probability and Statistics

This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.

Honors the path laid down by C.R. Rao and Arbind Kumar Lal Focuses on applications of data analytics to real-life problems and linear algebra to machine learning Discusses research in linear algebra, graphs, operator theory, game theory, and statistics

Autorentext
Ravindra B. Bapat is Visiting Professor at the Indian Statistical Institute, Delhi Center, New Delhi, India, where he earlier served for more than 35 years. He is also Adjunct Professor at the Manipal Academy of Higher Education (MAHE), Manipal, Karnataka, India. On the editorial board of the Indian Statistical Institute Series (a Springer book series), he is on the editorial board of several journals including Linear and Multilinear Algebra, AKCE International Journal of Graphs and Combinatorics, The Electronic Journal of Linear Algebra, and Indian Journal of Pure and Applied Mathematics. A contributor of more than 150 research articles, he has authored books, Linear Algebra and Linear Models (Springer, 2012) and Graphs and Matrices (Springer, 2010).

Manjunatha Prasad Karantha is Professor and Coordinator of the Center for Advanced Research in Applied Mathematics and Statistics at the Manipal Academy of Higher Education, Manipal, Karnataka, India. His research interests are in matrices over rings, generalized inverses, and matrix methods in graphs. He is on the editorial board of several reputed journals, published several research articles, and edited several books and special issues dedicated to the International Conference on Linear Algebra and its Applications series of conferences in reputed journals.

Stephen Kirkland is Professor at the Department of Mathematics and Associate Dean of the Faculty of Graduate Studies at the University of Manitoba, Canada. His research interests include non-negative matrix theory, spectral graph theory, and combinatorial matrix theory. For more than six years, he served as President of the International Linear Algebra Society. Besides being Editor-in-Chief of the Linear and Multilinear Algebra journal, he has been serving on editorial boards of journals, Linear Algebra and its Applications and the Electronic Journal of Linear Algebra.

S. K. Neogy is Professor at the Indian Statistical Institute and Head of its Delhi Center. He obtained his Ph.D. from the same institute, and his primary areas of research are mathematical programming, special matrices, and game theory. He is Co-editor of several books and special issues of several journals.

Sukanta Pati is Professor at the Indian Institute of Technology Guwahati, Assam, India. His research interests are in matrices in graphs. He is also on the editorial board of journals, Linear Multilinear Algebra, The Mathematics Student and Mathematics Newsletter.

Simo Puntanen is-after retirement-Visiting Researcher at Tampere University, Finland. He is Founding Member, with George P.H. Styan, of the International Workshop on Matrices and Statistics, held regularly from 1990 onwards. He is Co-author (with George P.H. Styan and Jarkko Isotalo) of the book, Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty (Springer, 2011).

Inhalt

Chapter 1. On Some Matrix Versions of Covariance, Harmonic Mean and other Inequalities: An Overview.- Chapter 2. The Impact of Professor C. R. Rao's Research used in solving problems in Applied Probability.- Chapter 3. Upper ounds for the Euclidean distances between the BLUEs under the partitioned linear fixed model and the corresponding mixed model.- Chapter 4. Nucleolus Computation for some Structured TU Games via Graph Theory and Linear Algebra.- Chapter 5. From Linear System of Equations to Artificial Intelligence - The evolution Journey of Computer Tomographic Image Reconstruction Algorithms.- Chapter 6. Shapley Value and other Axiomatic Extensions to Shapley Value.- Chapter 7. An Accelerated Block Randomized Kaczmarz Methos.- Chapter 8. Nullity of Graphs - A Survey and Some New Results.- Chapter 9. Some Observations on Algebraic Connectivity of Graphs.- Chapter 10. Orthogonality for iadjoints f Operators.- Chapter 11. Permissible covariance structures for simultaneous retention of BLUEs in small and big linear models.- Chapter 12. On some Special Matrices and its Applications in Linear Complementarity Problem.- Chapter 3. On Nearest Matrix with Partially Specified Eigen Structure.- Chapter 14. Equality of BLUEs for Full, Small, and Intermediate Linear Models under Covariance Change, with links to Data Confidentiality and Encryption.-Chapter 15. Statistical Inference for Middle Censored Data with Applications. etc