Richard A. Brualdi, Herbert J. Ryser, Brualdi Richard a.

Combinatorial Matrix Theory

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 380
• Erscheinungstermin: 29. September 2003
• Englisch
• Abmessung: 235mm x 157mm x 27mm
• Gewicht: 766g
• ISBN-13: 9780521322652
• ISBN-10: 0521322650
• Artikelnr.: 21557161

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)