Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications Book 39) 1st Edition by Richard A. Brualdi (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Sadly the authors have opted for a levelof abstraction that obscures many of thebeautiful details. Particularly disappointingis the last chapter on matrix theory which veersoff into an odd mixture of marginalia which havealmost no applications.

⭐This book is an excellent resource for mathematicians, computer scientists, and engineers. The book shows how to use zero-one matrices and stochastic matrices in your work. The text pretty shows a lot of interesting properties different matrices have and how to compute various values associated with graphs from them. The book would be very useful for people interested in Neural Networks, Speech Recognition, Artificial Intelligence. It is mathematics, though and it describes the properties of the matrices and contains many proofs about these properties. Make sure that you have mastered linear algebra and combinatorics before reading this text.

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Keywords

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Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications Book 39) 1st Edition PDF Free Download
Download Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications Book 39) 1st Edition 1991 PDF Free
Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications Book 39) 1st Edition 1991 PDF Free Download
Download Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications Book 39) 1st Edition PDF
Free Download Ebook Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications Book 39) 1st Edition