Focusing on the application of linear algebra to graph theory, this new edition highlights matrix techniques more extensively than other texts in the field. It provides in-depth coverage of key matrices related to graphs, including incidence, adjacency, and Laplacian matrices, illustrating their significance and utility in the study of graphs.
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 `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.
Focusing on a matrix theory perspective, this comprehensive introduction to linear algebra emphasizes its applications in statistics. The fully revised third edition explores essential topics such as rank additivity and singular values, providing a clear and concise understanding of the subject. Ideal for students and professionals alike, it serves as a valuable resource for mastering linear algebra concepts relevant to statistical analysis.