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Combinatorial Matrix Theory and Generalized Inverses of Matrices

  • Ravindra B. Bapat
  • Steve J. Kirkland
  • K. Manjunatha Prasad
  • Simo Puntanen

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Murali K. Srinivasan
    Pages 13-31
  3. R. B. Bapat, Sivaramakrishnan Sivasubramanian
    Pages 33-40
  4. K. Manjunatha Prasad, G. Sudhakara, H. S. Sujatha, M. Vinay
    Pages 41-55
  5. Tõnu Kollo, Anne Selart, Helle Visk
    Pages 63-72
  6. Jan Hauke, Augustyn Markiewicz, Simo Puntanen
    Pages 73-83
  7. Francisco Carvalho, João Tiago Mexia
    Pages 85-100
  8. Oskar Maria Baksalary, Götz Trenkler
    Pages 101-118
  9. Shani Jose, K. C. Sivakumar
    Pages 119-131
  10. Sachindranath Jayaraman
    Pages 133-141
  11. K. P. Deepesh, S. H. Kulkarni, M. T. Nair
    Pages 143-158
  12. Adel Alahmedi, Yousef Alkhamees, S. K. Jain
    Pages 177-181
  13. AR. Meenakshi
    Pages 183-193
  14. K. Manjunatha Prasad, K. S. Mohana, Y. Santhi Sheela
    Pages 195-226
  15. George P. H. Styan, Ka Lok Chu
    Pages 227-252
  16. R. B. Bapat, K. Manjunatha Prasad
    Pages 253-274
  17. Back Matter
    Pages 275-277

About this book

Introduction

This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs,

q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix,

copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on

old magic squares from India.

Keywords

Energy of Graph Generalized Inverse Linear Regression Model, Magic Square Matrix Methods in Graphs Partial Order on Matrices Spectrum of Graph

Editors and affiliations

  • Ravindra B. Bapat
    • 1
  • Steve J. Kirkland
    • 2
  • K. Manjunatha Prasad
    • 3
  • Simo Puntanen
    • 4
  1. 1.Indian Statistical InstituteNew DelhiIndia
  2. 2.Hamilton InstituteNational University of IrelandMaynoothIreland
  3. 3.Department of StatisticsManipal UniversityManipalIndia
  4. 4., School of Information SciencesUniversity of TampereTampereFinland

Bibliographic information