Combinatorial Matrix Theory and Generalized Inverses of Matrices

Editors: Bapat, R.B., Kirkland, S.J., Prasad, K.M., Puntanen, S. (Eds.)

  • Delves into two very important contemporary areas in linear algebra, namely combinatorial matrix theory and generalized inverses
  •  
  • Makes substantial advances in theory and application-oriented research in linear statistical inference
  •  
  • Covers a wide range of topics of interest such as graph theory, linear algebra, numerical methods and statistical inference
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Hardcover 94,99 €
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About this book

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.

About the authors

Ravindra B> Bapat is a Professor at the Indian Statistical Institute, Delhi Centre. He is a Fellow of the Indian Academy of Sciences, Indian National Science Academy and a J.C. Bose Fellow. He served as the President of the Indian Mathematical Society during 2007-2008. He has been on the editorial boards of Linear and Multilinear Algebra, Electronic Journal of Linear Algebra, India Journal of Pure and Applied Mathematics and Kerala Mathematical Association Bulletin.

Steve J.  Kirkland is a Stokes Professor at the National University of Ireland Maynooth. He is currently an Editor-in-Chief of the Journal Linear and Multilinear Algebra, and serves on the editorial boards of Linear Algebra and its Applications, the Electronic Journal of Linear Algebra, and SIAM Review. He is also the President of the International Linear Algebra Society.

K. Manjunatha Prasad is a Professor of Mathematics at the Department of Statistics, Manipal University, Manipal. He has several publications in the area of his research interest. His research interests are in matrix theory, generalized inverses, ring theory, projective modules and matrices in graph theory.

Simo Puntanen earned his PhD in Statistics from the University of Tampere (Finland) in 1987, where he is presently a Docent and Lecturer of Statistics. He was a Senior Fellow at the Academy of Finland (autumn 1988 and 1993 - 1995), an Associate Professor at Tampere University during 1997 - 1998 and worked as a Senior Scientist of the Academy in 1998 - 1999. He is currently the book review editor of the International Statistical Review.

Reviews

From the reviews:

“This book contains eighteen papers in the field of matrices in graph theory, generalised inverses of matrices, and matrix methods in statistics, written by leading mathematicians and statisticians. … the book covers a wide range of topics with substantial advances and is a welcome volume.” (Shuangzhe Liu, International Statistical Review, Vol. 82 (1), 2014)

Table of contents (19 chapters)

  • Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube

    Anuradha, A. (et al.)

    Pages 1-12

    Preview Buy Chapter 24,95 €
  • Notes on Explicit Block Diagonalization

    Srinivasan, Murali K.

    Pages 13-31

    Preview Buy Chapter 24,95 €
  • The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs

    Bapat, R. B. (et al.)

    Pages 33-40

    Preview Buy Chapter 24,95 €
  • Matrix Product of Graphs

    Manjunatha Prasad, K. (et al.)

    Pages 41-55

    Preview Buy Chapter 24,95 €
  • Determinant of the Laplacian Matrix of a Weighted Directed Graph

    Kalita, Debajit

    Pages 57-62

    Preview Buy Chapter 24,95 €

Buy this book

eBook 79,72 €
price for India (gross)
  • ISBN 978-81-322-1053-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 94,99 €
price for India (gross)
  • ISBN 978-81-322-1052-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 94,99 €
price for India (gross)
  • ISBN 978-81-322-1725-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Combinatorial Matrix Theory and Generalized Inverses of Matrices
Editors
  • Ravindra B. Bapat
  • Steve J. Kirkland
  • K. Manjunatha Prasad
  • Simo Puntanen
Copyright
2013
Publisher
Springer India
Copyright Holder
Springer India
eBook ISBN
978-81-322-1053-5
DOI
10.1007/978-81-322-1053-5
Hardcover ISBN
978-81-322-1052-8
Softcover ISBN
978-81-322-1725-1
Edition Number
1
Number of Pages
XVII, 277
Number of Illustrations and Tables
17 b/w illustrations, 36 illustrations in colour
Topics