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Combinatorial Matrix Theory
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Artikel-Nr:
9780521322652
Veröffentl:
2003
Einband:
HC gerader Rücken kaschiert
Erscheinungsdatum:
29.09.2003
Seiten:
380
Autor:
Richard A. Brualdi
Gewicht:
768 g
Format:
235x157x27 mm
Sprache:
Englisch
Beschreibung:
The book deals with the many connections between matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorical properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix and Latin squares. The book ends by considering algebraic characterizations of combinatorical properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jorda Canonical Form.
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.