Combinatorial matrix theory:
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 numbe...
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| Main Author: | |
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| Other Authors: | |
| Format: | eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1991
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| Series: | Encyclopedia of mathematics and its applications
volume 39 |
| Links: | https://doi.org/10.1017/CBO9781107325708 |
| Summary: | 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. |
| Physical Description: | 1 Online-Ressource (ix, 367 Seiten) |
| ISBN: | 9781107325708 |
Staff View
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| 520 | |a 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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| spelling | Brualdi, Richard A. Combinatorial matrix theory Richard A. Brualdi, Herbert J. Ryser Cambridge Cambridge University Press 1991 1 Online-Ressource (ix, 367 Seiten) txt c cr Encyclopedia of mathematics and its applications volume 39 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. Ryser, Herbert John Erscheint auch als Druck-Ausgabe 9780521322652 Erscheint auch als Druck-Ausgabe 9781107662605 |
| spellingShingle | Brualdi, Richard A. Combinatorial matrix theory |
| title | Combinatorial matrix theory |
| title_auth | Combinatorial matrix theory |
| title_exact_search | Combinatorial matrix theory |
| title_full | Combinatorial matrix theory Richard A. Brualdi, Herbert J. Ryser |
| title_fullStr | Combinatorial matrix theory Richard A. Brualdi, Herbert J. Ryser |
| title_full_unstemmed | Combinatorial matrix theory Richard A. Brualdi, Herbert J. Ryser |
| title_short | Combinatorial matrix theory |
| title_sort | combinatorial matrix theory |
| work_keys_str_mv | AT brualdiricharda combinatorialmatrixtheory AT ryserherbertjohn combinatorialmatrixtheory |