Richard A. Brualdi

Combinatorial Matrix Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book, first published in 1991, is devoted to the exposition of combinatorial matrix theory. This subject concerns itself with the use of matrix theory and linear algebra in proving results in combinatorics (and vice versa), and with the intrinsic properties of matrices viewed as arrays of numbers rather than algebraic objects in themselves. There are chapters dealing with the many connections between matrices, graphs, digraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorial properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix, and Latin squares. The final chapter deals with algebraic characterizations of combinatorial properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jordan Canonical Form. The book is sufficiently self-contained for use as a graduate course text, but complete enough for a standard reference work on the basic theory. Thus it will be an essential purchase for combinatorialists, matrix theorists, and those numerical analysts working in numerical linear algebra.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 26. Juli 1991
• Englisch
• ISBN-13: 9781107108028
• Artikelnr.: 53057674

Autorenporträt

Richard A. Brualdi is an Emeritus Professor at the University of Wisconsin in Madison, WI, USA. Pauline van den Driessche is an Emeritus Professor at the University of Victoria, Canada. Dragan Stevanovi¿ is a Full Research Professor at the Serbian Academy of Sciences and Arts in Belgrade, Serbia. Stephen Kirkland is a Professor at the University of Manitoba in Winnipeg, Canada. Ángeles Carmona is an Associate Professor at the Universitat Politècnica de Catalunya in Barcelona, Spain. 

Inhaltsangabe

1. Incidence matrices
2. Matrices and graphs
3. Matrices and digraphs
4. Matrices and bigraphs
5. Combinatorial matrix algebra
6. Existence theorems for combinatorially constrained matrices
7. Some special graphs
8. The permanent
9. Latin squares.

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Some combinatorially defined matrix class.- Sign pattern matrices.- The spectral radius of a graph.- The group inverse of the Laplacian matrix of a graph.- Boundary value problems on finite networks.

Rezensionen

"A very excellent treatment of the subject for mathematicians interested in the intersection between matrix theory and combinatorics. ... it is appropriate for graduate students and others interested in the latest developments in this rich and diverse field." (MAA Reviews, March 1, 2020)