Combinatorial Matrix Theory and Generalized Inverses of Matrices

Skew Spectrum of the Cartesian Product of an Oriented Graph with an Oriented Hypercube.- Notes on Explicit Block Diagonalization.- The Third Immanant of q-Laplacian Matrices of Trees and Laplacians of Regular Graphs.- Matrix Product of Graphs.- Determinant of the Laplacian Matrix of Weighted Directed Graphs .- From Multivariate Skewed Distributions to Copulas.- Revisiting the BLUE in a Linear Model via Proper Eigenvectors.- Inference in Error Orthogonal Models.- On the Entries of Orthogonal Projection Matrices.- Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces.- The Reverse Order Law in Indefinite Inner Product Spaces.- Generalized Inverses and Approximation Numbers.- On the Level-2 Condition Number for Moore-Penrose Inverse in Hilbert Space.- Products and Sums of Idempotent Matrices over Principal Ideal Domain.- Perfect Semiring of Nonnegative Matrices.- Regular Matrices over an Incline.- Matrix Partial Orders associated with Space Preorder.- An Illustrated Introductionto Some Old Magic Squares from India.- Appendix: Report on CMTGIM 2012, Manipal.- Index

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.

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)