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| 內容簡介： |
his book addresses recent developments in sign patterns for generalized inverses. The fundamental importance of the fields is obvious， since they are related with qualitative analysis of linear systems and combinatorial matrix theory.
The book provides both introductory materials and discussions to the areas in sign patterns for Moore-Penrose inverse， Drazin inverse and tensors. It is intended to convey results to the senior students and readers in pure and applied linear algebra， and combinatorial matrix theory.
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| 目錄：
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Contents
Preface III
Notations V
CHAPTER 1
Generalized Inverses 1
1.1 Matrix Decompositions 1
1.2 Moore-Penrose Inverse 2
1.3 Drazin Inverse 5
1.4 Group Inverse 8
1.5 Generalized Inverses and System of Linear Equations 12
1.6 Graph and Matrix 14
CHAPTER 2
Generalized Inverses of Partitioned Matrices 19
2.1 Drazin Inverse of Partitioned Matrices 19
2.2 Group Inverse of Partitioned Matrices 45
2.3 Additive Formulas for Drazin Inverse and Group Inverse 71
2.4 Drazin Inverse Index for Partitioned Matrices 96
CHAPTER 3
SNS and S2NS Matrices 101
3.1 Sign-Solvability of Linear Equations 101
3.2 Characterizations for SNS and S2NS Matrices via Digraphs 108
3.3 Ray Nonsingular and Ray S2NS Matrices 116
CHAPTER 4
Sign Pattern for Moore-Penrose Inverse 123
4.1 Least Squares Sign-Solvability 123
4.2 Matrices with Signed Moore-Penrose Inverse 125
4.3 Triangular Partitioned Matrices with Signed Moore-Penrose Inverse 138
4.4 Ray Pattern for Moore-Penrose Inverse 143
CHAPTER 5
Sign Pattern for Drazin Inverse 149
5.1 Matrices with Signed Drazin Inverse 149
5.2 Upper Triangular Partitioned Matrices with Signed Drazin Inverse 151
5.3 Anti-Triangular Partitioned Matrices with Signed Drazin Inverse 161
5.4 Bipartite Matrices with Signed Drazin Inverse 171
5.5 Sign Pattern of Group Inverse 176
5.6 Ray Pattern of Drazin Inverse 187
CHAPTER 6
Sign Pattern for Tensors 197
6.1 Tensors 197
6.2 Inverse of Tensors 200
6.3 Minimum and Maximum Rank of Sign Pattern Tensors 204
6.4 Sign Nonsingular Tensors 208
References 215
Book list of the Series in Information and Computational Science 225
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