The first chapter of this book provides a brief treatment of the basics of the subject. The other chapters deal with the various decompositions of non-negative matrices, Birkhoff type theorems, the study of the powers of non-negative matrices, applications of matrix methods to other combinatorial problems, and applications of combinatorial methods to matrix problems and linear algebra problems. The coverage of prerequisites has been kept to a minimum. Nevertheless, the book is basically self-contained (an Appendix provides the necessary background in linear algebra, graph theory and combinatorics). There are many exercises, all of which are accompanied by sketched solutions. Audience: The book is suitable for a graduate course as well as being an excellent reference and a valuable resource for mathematicians working in the area of combinatorial matrix theory.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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minimally strong digraph, primitive digraph, indecomposable exponent, undirected star, bipartite decomposition, bipartite digraph representation, complementary acyclic, cospectral graphs, indecomposable matrices, singular vertices, cocycle space, primitive matrices, indecomposable matrix, orthonormal representation, partite sets, reducible matrix, associated digraph, reducible matrices, band graph, singular vertex, permutation equivalent, irreducible block, directed walk, primitive matrix, directed cycle Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Sketch of Proof, Combinatorial Problems, Prove Lemma, Proof Note, Prove Corollary, Combinatorial Analysis, Combinatorial Properties of Matrices, Exercises Exercise, Proof Assume, Proof Suppose, Proof By Theorem, Prove Proposition, Apply Corollary, Proof By Proposition New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
minimally strong digraph, primitive digraph, indecomposable exponent, undirected star, bipartite decomposition, bipartite digraph representation, complementary acyclic, cospectral graphs, indecomposable matrices, singular vertices, cocycle space, primitive matrices, indecomposable matrix, orthonormal representation, partite sets, reducible matrix, associated digraph, reducible matrices, band graph, singular vertex, permutation equivalent, irreducible block, directed walk, primitive matrix, directed cycle Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Sketch of Proof, Combinatorial Problems, Prove Lemma, Proof Note, Prove Corollary, Combinatorial Analysis, Combinatorial Properties of Matrices, Exercises Exercise, Proof Assume, Proof Suppose, Proof By Theorem, Prove Proposition, Apply Corollary, Proof By Proposition New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 23
books:
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5
books
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- Graph Theory (Graduate Texts in Mathematics) by Reinhard Diestel on 4 pages
- Linear Algebra by Jin Ho Kwak in Back Matter (1), Back Matter (2), and Back Matter (3)
- Linear Algebra (2nd Edition) by Kenneth M Hoffman in Back Matter (1), Back Matter (2), and Back Matter (3)
- Linear Algebra (Oxford Science Publications) by Richard Kaye in Back Matter (1), and Back Matter (2)
- Selected Topics in Graph Theory by Lowell W. Beineke in Back Matter (1), and Back Matter (2)
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- Theory and Application of Graphs (Network Theory and Applications) by Junming Xu on page 77, and Back Matter
- Optical Networks: Recent Advances (Network Theory and Applications) by Lu Ruan in Back Matter
- Reliabilities of Consecutive-k Systems (Network Theory and Applications, Volume 4) by G. Chang in Back Matter
- Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory by Dennis S. Bernstein in Back Matter
- Multiwavelength Optical Networks (Network Theory and Applications) by Xiaohua Jia in Back Matter
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