Matrices and Matroids for Systems Analysis

By: Kazuo Murota

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Hardcover | 1 January 2000

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500 Pages

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24.77 x 16.51 x 3.18

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A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis.

This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems.

This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science.

From the reviews:

"...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students."

Andras Recski, Mathematical Reviews Clippings 2000m:93006

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Preface
Introduction to Structural Approach - Overview of the Book	p. 1
Structural Approach to Index of DAE	p. 1
What Is Combinatorial Structure?	p. 10
Mathematics on Mixed Polynomial Matrices	p. 20
Matrix, Graph, and Matroid	p. 31
Matrix	p. 31
Graph	p. 43
Matroid	p. 71
Physical Observations for Mixed Matrix Formulation	p. 107
Mixed Matrix for Modeling Two Kinds of Numbers	p. 107
Algebraic Implication of Dimensional Consistency	p. 120
Physical Matrix	p. 126
Theory and Application of Mixed Matrices	p. 131
Mixed Matrix and Layered Mixed Matrix	p. 131
Rank of Mixed Matrices	p. 134
Structural Solvability of Systems of Equations	p. 153
Combinatorial Canonical Form of LM-matrices	p. 167
Irreducibility of LM-matrices	p. 202
Decomposition of Mixed Matrices	p. 211
Related Decompositions	p. 221
Partitioned Matrix	p. 230
Principal Structures of LM-matrices	p. 250
Polynomial Matrix and Valuated Matroid	p. 271
Polynomial/Rational Matrix	p. 271
Valuated Matroid	p. 280
Theory and Application of Mixed Polynomial Matrices	p. 331
Descriptions of Dynamical Systems	p. 331
Degree of Determinant of Mixed Polynomial Matrices	p. 335
Smith Form of Mixed Polynomial Matrices	p. 355
Controllability of Dynamical Systems	p. 364
Fixed Modes of Decentralized Systems	p. 384
Further Topics	p. 403
Combinatorial Relaxation Algorithm	p. 403
Combinatorial System Theory	p. 418
Mixed Skew-symmetric Matrix	p. 431
References	p. 453
Notation Table	p. 469
Index	p. 479
Table of Contents provided by Blackwell. All Rights Reserved.

Matrices and Matroids for Systems Analysis

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