Combinatorial Matrix Theory and Generalized Inverses of Matrices

✍ Scribed by A. Anuradha, R. Balakrishnan (auth.), Ravindra B. Bapat, Steve J. Kirkland, K. Manjunatha Prasad, Simo Puntanen (eds.)

• Publisher: Springer India
• Year: 2013
• Tongue: English
• Leaves: 281
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XVII
Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube....Pages 1-12
Notes on Explicit Block Diagonalization....Pages 13-31
The Third Immanant of q -Laplacian Matrices of Trees and Laplacians of Regular Graphs....Pages 33-40
Matrix Product of Graphs....Pages 41-55
Determinant of the Laplacian Matrix of a Weighted Directed Graph....Pages 57-62
From Multivariate Skewed Distributions to Copulas....Pages 63-72
Revisiting the BLUE in a Linear Model via Proper Eigenvectors....Pages 73-83
Inference in Error Orthogonal Models....Pages 85-100
On the Entries of Orthogonal Projection Matrices....Pages 101-118
Moore–Penrose Inverse of Perturbed Operators on Hilbert Spaces....Pages 119-131
The Reverse Order Law in Indefinite Inner Product Spaces....Pages 133-141
Generalized Inverses and Approximation Numbers....Pages 143-158
On the Level-2 Condition Number for Moore–Penrose Inverse in Hilbert Space....Pages 159-169
Products and Sums of Idempotent Matrices over Principal Ideal Domains....Pages 171-175
Perfect Semiring of Nonnegative Matrices....Pages 177-181
Regular Matrices over an Incline....Pages 183-193
Matrix Partial Orders Associated with Space Preorder....Pages 195-226
An Illustrated Introduction to Some Old Magic Squares from India....Pages 227-252
A Report on CMTGIM 2012, Manipal....Pages 253-274
Back Matter....Pages 275-277

✦ Subjects

Linear and Multilinear Algebras, Matrix Theory; Statistical Theory and Methods