Matrices and matroids for systems analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Algorithms and combinatorics
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 483 S. graph. Darst. |
| ISBN: | 3540660240 |
Staff View
MARC
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| 245 | 1 | 0 | |a Matrices and matroids for systems analysis |c Kazuo Murota |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a XII, 483 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804127479068098560 |
|---|---|
| adam_text | Contents
Preface V
1. Introduction to Structural Approacn — Overview of the
Book 1
1.1 Structural Approach to Index of DAE 1
1.1.1 Index of Differential algebraic Equations 1
1.1.2 Graph theoretic Structural Approach 3
1.1.3 An Embarrassing Phenomenon 7
1.2 What Is Combinatorial Structure? 10
1.2.1 Two Kinds of Numbers 11
1.2.2 Descriptor Form Rather than Standard Form 15
1.2.3 Dimensional Analysis 17
1.3 Mathematics on Mixed Polynomial Matrices 20
1.3.1 Formal Definitions 20
1.3.2 Resolution of the Index Problem 21
1.3.3 Block triangular Decomposition 26
2. Matrix, Graph, and Matroid 31
2.1 Matrix 31
2.1.1 Polynomial and Algebraic Independence 31
2.1.2 Determinant 33
2.1.3 Rank, Term rank and Generic rank 36
2.1.4 Block triangular Forms 40
2.2 Graph 43
2.2.1 Directed Graph and Bipartite Graph 43
2.2.2 Jordan Holder type Theorem for Submodular Functions 48
2.2.3 Dulmage Mendelsohn Decomposition 55
2.2.4 Maximum Flow and Menger type Linking 65
2.2.5 Minimum Cost Flow and Weighted Matching 67
2.3 Matroid 71
2.3.1 From Matrix to Matroid 71
2.3.2 Basic Concepts 73
2.3.3 Examples 77
2.3.4 Basis Exchange Properties 78
2.3.5 Independent Matching Problem 84
2.3.6 Union 93
2.3.7 Bimatroid (Linking System) 97
3. Physical Observations for Mixed Matrix Formulation 107
3.1 Mixed Matrix for Modeling Two Kinds of Numbers 107
3.1.1 Two Kinds of Numbers 107
3.1.2 Mixed Matrix and Mixed Polynomial Matrix 116
3.2 Algebraic Implication of Dimensional Consistency 120
3.2.1 Introductory Comments 120
3.2.2 Dimensioned Matrix 121
3.2.3 Total Unimodularity of a Dimensioned Matrix 123
3.3 Physical Matrix 126
3.3.1 Physical Matrix 126
3.3.2 Physical Matrices in a Dynamical System 128
4. Theory and Application of Mixed Matrices 131
4.1 Mixed Matrix and Layered Mixed Matrix 131
4.2 Rank of Mixed Matrices 134
4.2.1 Rank Identities for LM matrices 135
4.2.2 Rank Identities for Mixed Matrices 139
4.2.3 Reduction to Independent Matching Problems 142
4.2.4 Algorithms for the Rank 145
4.3 Structural Solvability of Systems of Equations 153
4.3.1 Formulation of Structural Solvability 153
4.3.2 Graphical Conditions for Structural Solvability 156
4.3.3 Matroidal Conditions for Structural Solvability 160
4.4 Combinatorial Canonical Form of LM matrices 167
4.4.1 LM equivalence 167
4.4.2 Theorem of CCF 172
4.4.3 Construction of CCF 175
4.4.4 Algorithm for CCF 181
4.4.5 Decomposition of Systems of Equations by CCF 187
4.4.6 Application of CCF 191
4.4.7 CCF over Rings 199
4.5 Irreducibility of LM matrices 202
4.5.1 Theorems on LM irreducibility 202
4.5.2 Proof of the Irreducibility of Determinant 205
4.6 Decomposition of Mixed Matrices 211
4.6.1 LU decomposition of Invertible Mixed Matrices 212
4.6.2 Block triangularization of General Mixed Matrices .... 215
4.7 Related Decompositions 221
4.7.1 Decomposition as Matroid Union 221
4.7.2 Multilayered Matrix 225
4.7.3 Electrical Network with Admittance Expression 228
4.8 Partitioned Matrix 230
4.8.1 Definitions 231
4.8.2 Existence of Proper Block triangularization 235
4.8.3 Partial Order Among Blocks 238
4.8.4 Generic Partitioned Matrix 240
4.9 Principal Structures of LM matrices 250
4.9.1 Motivations 250
4.9.2 Principal Structure of Submodular Systems 252
4.9.3 Principal Structure of Generic Matrices 254
4.9.4 Vertical Principal Structure of LM matrices 257
4.9.5 Horizontal Principal Structure of LM matrices 261
5. Polynomial Matrix and Valuated Matroid 271
5.1 Polynomial/Rational Matrix 271
5.1.1 Polynomial Matrix and Smith Form 271
5.1.2 Rational Matrix and Smith McMillan Form at Infinity 272
5.1.3 Matrix Pencil and Kronecker Form 275
5.2 Valuated Matroid 280
5.2.1 Introduction 280
5.2.2 Examples 281
5.2.3 Basic Operations 282
5.2.4 Greedy Algorithms 285
5.2.5 Valuated Bimatroid 287
5.2.6 Induction Through Bipartite Graphs 290
5.2.7 Characterizations 295
5.2.8 Further Exchange Properties 300
5.2.9 Valuated Independent Assignment Problem 306
5.2.10 Optimality Criteria 308
5.2.11 Application to Triple Matrix Product 316
5.2.12 Cycle canceling Algorithms 317
5.2.13 Augmenting Algorithms 325
6. Theory and Application of Mixed Polynomial Matrices . .. 331
6.1 Descriptions of Dynamical Systems 331
6.1.1 Mixed Polynomial Matrix Descriptions 331
6.1.2 Relationship to Other Descriptions 332
6.2 Degree of Determinant of Mixed Polynomial Matrices 335
6.2.1 Introduction 335
6.2.2 Graph theoretic Method 336
6.2.3 Basic Identities 337
6.2.4 Reduction to Valuated Independent Assignment 340
6.2.5 Duality Theorems 343
6.2.6 Algorithm 348
6.3 Smith Form of Mixed Polynomial Matrices 355
6.3.1 Expression of Invariant Factors 355
6.3.2 Proofs 363
6.4 Controllability of Dynamical Systems 364
6.4.1 Controllability 364
6.4.2 Structural Controllability 365
6.4.3 Mixed Polynomial Matrix Formulation 372
6.4.4 Algorithm 375
6.4.5 Examples 379
6.5 Fixed Modes of Decentralized Systems 384
6.5.1 Fixed Modes 384
6.5.2 Structurally Fixed Modes 387
6.5.3 Mixed Polynomial Matrix Formulation 390
6.5.4 Algorithm 395
6.5.5 Examples 398
7. Further Topics 403
7.1 Combinatorial Relaxation Algorithm 403
7.1.1 Outline of the Algorithm 403
7.1.2 Test for Upper tightness 407
7.1.3 Transformation Towards Upper tightness 413
7.1.4 Algorithm Description 417
7.2 Combinatorial System Theory 418
7.2.1 Definition of Combinatorial Dynamical Systems 419
7.2.2 Power Products 420
7.2.3 Eigensets and Recurrent Sets 422
7.2.4 Controllability of Combinatorial Dynamical Systems . . 426
7.3 Mixed Skew symmetric Matrix 431
7.3.1 Introduction 431
7.3.2 Skew symmetric Matrix 433
7.3.3 Delta matroid 438
7.3.4 Rank of Mixed Skew symmetric Matrices 444
7.3.5 Electrical Network Containing Gyrators 446
References 453
Notation Table 469
Index 479
|
| any_adam_object | 1 |
| author | Murota, Kazuo 1955- |
| author_GND | (DE-588)121432424 |
| author_facet | Murota, Kazuo 1955- |
| author_role | aut |
| author_sort | Murota, Kazuo 1955- |
| author_variant | k m km |
| building | Verbundindex |
| bvnumber | BV012806526 |
| callnumber-first | Q - Science |
| callnumber-label | QA166 |
| callnumber-raw | QA166.6 |
| callnumber-search | QA166.6 |
| callnumber-sort | QA 3166.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 |
| classification_tum | MSR 580f MAT 150f MAT 052f |
| ctrlnum | (OCoLC)42652687 (DE-599)BVBBV012806526 |
| dewey-full | 512.9/434 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/434 |
| dewey-search | 512.9/434 |
| dewey-sort | 3512.9 3434 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
| format | Book |
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| indexdate | 2024-07-09T18:34:00Z |
| institution | BVB |
| isbn | 3540660240 |
| language | English |
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| physical | XII, 483 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | Springer |
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| series | Algorithms and combinatorics |
| series2 | Algorithms and combinatorics |
| spelling | Murota, Kazuo 1955- Verfasser (DE-588)121432424 aut Matrices and matroids for systems analysis Kazuo Murota Berlin [u.a.] Springer 2000 XII, 483 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Algorithms and combinatorics 20 Combinatieleer gtt Configurações geométricas larpcal Matrices gtt Matroiden gtt Matroides larpcal Systeemtheorie gtt Matrices Matroids System analysis Matroid (DE-588)4128705-8 gnd rswk-swf Systemidentifikation (DE-588)4121753-6 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 gnd rswk-swf Matrix Mathematik (DE-588)4037968-1 s Matroid (DE-588)4128705-8 s Systemidentifikation (DE-588)4121753-6 s 1\p DE-604 DE-604 Algorithms and combinatorics 20 (DE-604)BV000617357 20 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008710407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Murota, Kazuo 1955- Matrices and matroids for systems analysis Algorithms and combinatorics Combinatieleer gtt Configurações geométricas larpcal Matrices gtt Matroiden gtt Matroides larpcal Systeemtheorie gtt Matrices Matroids System analysis Matroid (DE-588)4128705-8 gnd Systemidentifikation (DE-588)4121753-6 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| subject_GND | (DE-588)4128705-8 (DE-588)4121753-6 (DE-588)4037968-1 |
| title | Matrices and matroids for systems analysis |
| title_auth | Matrices and matroids for systems analysis |
| title_exact_search | Matrices and matroids for systems analysis |
| title_full | Matrices and matroids for systems analysis Kazuo Murota |
| title_fullStr | Matrices and matroids for systems analysis Kazuo Murota |
| title_full_unstemmed | Matrices and matroids for systems analysis Kazuo Murota |
| title_short | Matrices and matroids for systems analysis |
| title_sort | matrices and matroids for systems analysis |
| topic | Combinatieleer gtt Configurações geométricas larpcal Matrices gtt Matroiden gtt Matroides larpcal Systeemtheorie gtt Matrices Matroids System analysis Matroid (DE-588)4128705-8 gnd Systemidentifikation (DE-588)4121753-6 gnd Matrix Mathematik (DE-588)4037968-1 gnd |
| topic_facet | Combinatieleer Configurações geométricas Matrices Matroiden Matroides Systeemtheorie Matroids System analysis Matroid Systemidentifikation Matrix Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008710407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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