The Minimum Rank Inverse Inertia And Inverse Eigenvalue Problems For Graphs
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Author | : Mark Condie Kempton |
Publisher | : |
Total Pages | : 66 |
Release | : 2010 |
Genre | : |
ISBN | : |
Download The Minimum Rank, Inverse Inertia, and Inverse Eigenvalue Problems for Graphs Book in PDF, Epub and Kindle
For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.
Author | : Curtis G. Nelson |
Publisher | : |
Total Pages | : 0 |
Release | : 2012 |
Genre | : |
ISBN | : |
Download Diagonal Entry Restrictions in Minimum Rank Matrices, and the Inverse Inertia and Eigenvalue Problems for Graphs Book in PDF, Epub and Kindle
Author | : Leslie Hogben |
Publisher | : American Mathematical Society |
Total Pages | : 302 |
Release | : 2022-07-21 |
Genre | : Mathematics |
ISBN | : 1470466554 |
Download Inverse Problems and Zero Forcing for Graphs Book in PDF, Epub and Kindle
This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.
Author | : Moody Chu |
Publisher | : Oxford University Press |
Total Pages | : 408 |
Release | : 2005-06-16 |
Genre | : Mathematics |
ISBN | : 0198566646 |
Download Inverse Eigenvalue Problems Book in PDF, Epub and Kindle
Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.
Author | : Leslie Hogben |
Publisher | : CRC Press |
Total Pages | : 1906 |
Release | : 2013-11-26 |
Genre | : Mathematics |
ISBN | : 1498785603 |
Download Handbook of Linear Algebra Book in PDF, Epub and Kindle
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and
Author | : Ravindra B. Bapat |
Publisher | : Springer Science & Business Media |
Total Pages | : 175 |
Release | : 2010-07-23 |
Genre | : Mathematics |
ISBN | : 1848829817 |
Download Graphs and Matrices Book in PDF, Epub and Kindle
Graphs and Matrices provides a welcome addition to the rapidly expanding selection of literature in this field. As the title suggests, the book’s primary focus is graph theory, with an emphasis on topics relating to linear algebra and matrix theory. Information is presented at a relatively elementary level with the view of leading the student into further research. In the first part of the book matrix preliminaries are discussed and the basic properties of graph-associated matrices highlighted. Further topics include those of graph theory such as regular graphs and algebraic connectivity, Laplacian eigenvalues of threshold graphs, positive definite completion problem and graph-based matrix games. Whilst this book will be invaluable to researchers in graph theory, it may also be of benefit to a wider, cross-disciplinary readership.
Author | : Gene H. Golub |
Publisher | : JHU Press |
Total Pages | : 781 |
Release | : 2013-02-15 |
Genre | : Mathematics |
ISBN | : 1421407949 |
Download Matrix Computations Book in PDF, Epub and Kindle
This revised edition provides the mathematical background and algorithmic skills required for the production of numerical software. It includes rewritten and clarified proofs and derivations, as well as new topics such as Arnoldi iteration, and domain decomposition methods.
Author | : Moody Ten-Chao Chu |
Publisher | : |
Total Pages | : |
Release | : 2001 |
Genre | : |
ISBN | : |
Download Inverse Eigenvalue Problems Book in PDF, Epub and Kindle
Author | : Michiel Hazewinkel |
Publisher | : Springer Science & Business Media |
Total Pages | : 638 |
Release | : 1997-08-31 |
Genre | : Mathematics |
ISBN | : 9780792347095 |
Download Encyclopaedia of Mathematics Book in PDF, Epub and Kindle
This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.
Author | : Olga Azenhas |
Publisher | : |
Total Pages | : 190 |
Release | : 2006 |
Genre | : Algebras, Linear |
ISBN | : |
Download Mathematical Papers in Honour of Eduardo Marques de Sa Book in PDF, Epub and Kindle