《矩陣空間的保持問題(英文版)》介紹矩陣論的一個研究領域----保持問題。主要內容包括最小秩保持、秩加性保持、秩等價保持、平方零保持、k-冪保持、k-冪等保持、矩陣(廣義)逆保持、對合保持、伴隨保持、乘積保持等。
基本介紹
- 書名：矩陣空間的保持問題
- 出版社：科學出版社有限責任公司
- 頁數：409頁
- 開本：16
- 定價：80.00
- 作者：張顯
- 出版日期：2007年6月7日
- 語種：英語
- ISBN：7030189310, 9787030189318
- 品牌：科學出版社
內容簡介,圖書目錄,
內容簡介
《矩陣空間的保持問題(英文版)》：One of the very active research areas in matrix theory is the study of preserver problems,including linear preserver problems,additive preserver problems and multiplicative preserver problems,which concern the classification of maps on matrices or operators that preserve certain special properties.
圖書目錄
Preface
Notation
Chapter 1 Introduction to preserver problems
1.1 Definitions
1.2 Typical categories of preserver problems
1.3 Techniques of Preserver Problems
1.4 Organization
Chapter 2 Preservers of the smallest nonzero rank
2.1 Additive rank-1 preservers between spaces of rectangular matrices
2.2 Additive rank-1 preservers between spaces of symmetric matrices
2.3 Additive rank-1 preservers between spaces of Hermitian matrices
2.4 Additive rank-1 preservers from a space of triangular matrices to a space of square matrices
2.5 Additive rank-2 preservers between spaces of alternate matrices
2.6 Invertible linear rank-1 preservers on spaces of trace zero matrices
2.7 Invertibility (characteristic polynomial,determinant) preservers
2.8 Remarks on Chapter 2
Chapter 3 Additive rank-additivity preservers and applications
3.1 Additive rank-additivity preservers on spaces of rectangular matrices
3.2 Additive rank-additivity preservers on spaces of symmetric matrices
3.3 Additive rank-additivity preservers on spaces of Hermitian matrices
3.4 Additive rank-additivity preservers on spaces of alternate matrices
3.5 Applications of additive rank-additivity preservers
3.6 Remarks on Chapter 3
Chapter 4 Additive preservers of rank equivalence and applications
4.1 Main results
4.2 Proofs of main results
4.3 Remarks on Chapter 4
Chapter 5 Linear square-zero preservers on spaces of square matrices
5.1 Main results
5.2 Proofs of main results
5.3 Remarks on Chapter 5
Chapter 6 Preservers of k-power/k-potent
6.1 Additive preservers of idempotence between spaces of square matrices
6.2 Injective additive preservers of idempotence on spaces of triangular matrices
6.3 Linear preservers of idempotence between spaces of symmetric matrices
6.4 Several problems related to k-power and k-potent preservers
6.5 Preservers of k-power
6.6 Preservers of k-potent matrices
6.7 Jordan homomorphisms between of rings of square matrices
6.8 Preservers of idempotent relation
6.9 Remarks on Chapter 6
Chapter 7 Preservers of inverses of matrices
7.1 Linear inverse preservers between spaces of matrices
7.2 Additive inverse preservers between spaces of matrices
7.3 Remarks on Chapter 7
Chapter 8 Preservers of generalized inverses of matrices
8.1 Additive preservers of M-P inverses of matrices over fields
8.2 Additive preservers of {1,2}-inverses of matrices over fields
8.3 Additive preservers of group inverses of matrices over fields
8.4 Strong linear preservers of Moore-Penrose inverses of matrices over the two-element Boolean algebra
8.5 Covariant operator pairs on M-P Inverses of matrices between real finite dimensional division algebras
8.6 Remarks on Chapter 8
Chapter 9 Linear preservers of involutory matrices
9.1 Main results
9.2 Proofs of main results
9.3 Remarks on Chapter 9
Chapter 10 Additive adjoint preservers
10.1 Main results
10.2 Proofs of main results
10.3 Remarks on Chapter 10
Chapter 11 Preservers of multiplication
11.1 Homomorphisms from one general linear group to another
11.2 Homomorphisms from a multiplicative matrix semigroup to another
11.3 Automorphisms of multiplicative semigroups of upper triangular matrices
11.4 Remarks on Chapter 11
Appendix A Fitting decomposition of a matrix
Appendix B Canonical form of a rank-additive matrix pair
Appendix C Canonical form of a matrix triple
Appendix D Adjoint matrices
Bibliography
Index
Notation
Chapter 1 Introduction to preserver problems
1.1 Definitions
1.2 Typical categories of preserver problems
1.3 Techniques of Preserver Problems
1.4 Organization
Chapter 2 Preservers of the smallest nonzero rank
2.1 Additive rank-1 preservers between spaces of rectangular matrices
2.2 Additive rank-1 preservers between spaces of symmetric matrices
2.3 Additive rank-1 preservers between spaces of Hermitian matrices
2.4 Additive rank-1 preservers from a space of triangular matrices to a space of square matrices
2.5 Additive rank-2 preservers between spaces of alternate matrices
2.6 Invertible linear rank-1 preservers on spaces of trace zero matrices
2.7 Invertibility (characteristic polynomial,determinant) preservers
2.8 Remarks on Chapter 2
Chapter 3 Additive rank-additivity preservers and applications
3.1 Additive rank-additivity preservers on spaces of rectangular matrices
3.2 Additive rank-additivity preservers on spaces of symmetric matrices
3.3 Additive rank-additivity preservers on spaces of Hermitian matrices
3.4 Additive rank-additivity preservers on spaces of alternate matrices
3.5 Applications of additive rank-additivity preservers
3.6 Remarks on Chapter 3
Chapter 4 Additive preservers of rank equivalence and applications
4.1 Main results
4.2 Proofs of main results
4.3 Remarks on Chapter 4
Chapter 5 Linear square-zero preservers on spaces of square matrices
5.1 Main results
5.2 Proofs of main results
5.3 Remarks on Chapter 5
Chapter 6 Preservers of k-power/k-potent
6.1 Additive preservers of idempotence between spaces of square matrices
6.2 Injective additive preservers of idempotence on spaces of triangular matrices
6.3 Linear preservers of idempotence between spaces of symmetric matrices
6.4 Several problems related to k-power and k-potent preservers
6.5 Preservers of k-power
6.6 Preservers of k-potent matrices
6.7 Jordan homomorphisms between of rings of square matrices
6.8 Preservers of idempotent relation
6.9 Remarks on Chapter 6
Chapter 7 Preservers of inverses of matrices
7.1 Linear inverse preservers between spaces of matrices
7.2 Additive inverse preservers between spaces of matrices
7.3 Remarks on Chapter 7
Chapter 8 Preservers of generalized inverses of matrices
8.1 Additive preservers of M-P inverses of matrices over fields
8.2 Additive preservers of {1,2}-inverses of matrices over fields
8.3 Additive preservers of group inverses of matrices over fields
8.4 Strong linear preservers of Moore-Penrose inverses of matrices over the two-element Boolean algebra
8.5 Covariant operator pairs on M-P Inverses of matrices between real finite dimensional division algebras
8.6 Remarks on Chapter 8
Chapter 9 Linear preservers of involutory matrices
9.1 Main results
9.2 Proofs of main results
9.3 Remarks on Chapter 9
Chapter 10 Additive adjoint preservers
10.1 Main results
10.2 Proofs of main results
10.3 Remarks on Chapter 10
Chapter 11 Preservers of multiplication
11.1 Homomorphisms from one general linear group to another
11.2 Homomorphisms from a multiplicative matrix semigroup to another
11.3 Automorphisms of multiplicative semigroups of upper triangular matrices
11.4 Remarks on Chapter 11
Appendix A Fitting decomposition of a matrix
Appendix B Canonical form of a rank-additive matrix pair
Appendix C Canonical form of a matrix triple
Appendix D Adjoint matrices
Bibliography
Index
