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Matrices and Matroids for Systems Analysis : Algorithms and Combinatorics - Kazuo Murota

Matrices and Matroids for Systems Analysis

Algorithms and Combinatorics

Hardcover Published: January 2000
ISBN: 9783540660248
Number Of Pages: 483

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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 last decade. 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.

Preface
Introduction to Structural Approach - Overview of the Bookp. 1
Structural Approach to Index of DAEp. 1
What Is Combinatorial Structure?p. 10
Mathematics on Mixed Polynomial Matricesp. 20
Matrix, Graph, and Matroidp. 31
Matrixp. 31
Graphp. 43
Matroidp. 71
Physical Observations for Mixed Matrix Formulationp. 107
Mixed Matrix for Modeling Two Kinds of Numbersp. 107
Algebraic Implication of Dimensional Consistencyp. 120
Physical Matrixp. 126
Theory and Application of Mixed Matricesp. 131
Mixed Matrix and Layered Mixed Matrixp. 131
Rank of Mixed Matricesp. 134
Structural Solvability of Systems of Equationsp. 153
Combinatorial Canonical Form of LM-matricesp. 167
Irreducibility of LM-matricesp. 202
Decomposition of Mixed Matricesp. 211
Related Decompositionsp. 221
Partitioned Matrixp. 230
Principal Structures of LM-matricesp. 250
Polynomial Matrix and Valuated Matroidp. 271
Polynomial/Rational Matrixp. 271
Valuated Matroidp. 280
Theory and Application of Mixed Polynomial Matricesp. 331
Descriptions of Dynamical Systemsp. 331
Degree of Determinant of Mixed Polynomial Matricesp. 335
Smith Form of Mixed Polynomial Matricesp. 355
Controllability of Dynamical Systemsp. 364
Fixed Modes of Decentralized Systemsp. 384
Further Topicsp. 403
Combinatorial Relaxation Algorithmp. 403
Combinatorial System Theoryp. 418
Mixed Skew-symmetric Matrixp. 431
Referencesp. 453
Notation Tablep. 469
Indexp. 479
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540660248
ISBN-10: 3540660240
Series: Algorithms and Combinatorics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 483
Published: January 2000
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.69
Weight (kg): 0.87

Earn 542 Qantas Points
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