书目详细信息
： Algebraic theory of generalized inverses /
书目信息 机读格式(MARC)
| ISBN： | 9787030765703 |
|---|---|
| 编目源： | TJDX TJDX PUL |
| 个人名称： | Chen, Jianlong |
| 题名： | Algebraic theory of generalized inverses / Jianlong Chen, Xiaoxiang Zhang = 广义逆的代数理论 / 陈建龙, 张小向. |
| 载体形态： | ix, 322 pages ; 25 cm. |
| 书目附注： | Includes bibliographical references (pages 315-320) and index. |
| 格式化内容附注： | Intro -- Preface -- Contents -- 1 Algebraic Basic Knowledge -- 1.1 Complex Matrices -- 1.1.1 Some Decompositions of Complex Matrices -- 1.1.2 The Index of a Square Complex Matrix -- 1.1.3 Idempotents, Projections and EP Matrices -- 1.2 Definitions and Examples of Rings -- 1.2.1 Basic Concepts and Examples -- 1.2.2 Some Extensions of Rings -- 1.2.3 Idempotents, Units and Regular Elements -- 1.2.4 One-Sided Invertibility and Invertibility -- 1.3 Semigroups, Rings and Categories with Involution -- 1.3.1 Definitions and Examples -- 1.3.2 Proper Involutions -- 1.3.3 The Gelfand-Naimark Property -- 1.4 Regularity and -Regularity of Rings -- 1.4.1 Regularity and FP-Injectivity -- 1.4.2 -Regularity -- 1.5 Invertibility of the Difference and the Sum of Idempotents -- 1.5.1 Invertibility of the Difference of Idempotents -- 1.5.2 Invertibility of the Sum of Idempotents -- 2 Moore-Penrose Inverses -- 2.1 Moore-Penrose Inverses of Complex Matrices -- 2.2 Characterizations of Moore-Penrose Inverses of Elements in Semigroups or Rings -- 2.2.1 Moore-Penrose Inverses of Elements in a Semigroup -- 2.2.2 Moore-Penrose Inverses of Elements in a Ring -- 2.2.3 Moore-Penrose Inverses of Matrices over a Ring -- 2.3 The Moore-Penrose Inverse of a Product -- 2.3.1 The Moore-Penrose Inverse of a Product paq -- 2.3.2 The Moore-Penrose Inverse of a Matrix Product -- 2.4 Moore-Penrose Inverses of Differences and Productsof Projections -- 2.5 Jacobson's Lemma for Moore-Penrose Inverses -- 2.5.1 Jacobson's Lemma for Moore-Penrose Inverses in a (Generalized) GN Ring -- 2.5.2 Jacobson's Lemma for Moore-Penrose Inverses in a Ring -- 2.6 The Moore-Penrose Inverse of a 22 Block Matrix -- 2.7 The Moore-Penrose Inverse of a Companion Matrix -- 2.8 The Moore-Penrose Inverse of a Sum of Morphisms -- 3 Group Inverses -- 3.1 Group Inverses of Complex Matrices -- 3.2 Characterizations of Group Inverses of Elements in Semigroups and Rings -- 3.3 The Group Inverse of a Product paq -- 3.4 The Group Inverse of a Sum of Morphisms -- 3.5 The Group Inverse of the Sum of Two Group Invertible Elements -- 3.6 The Group Inverse of the Product of Two Regular Elements -- 3.7 Group Inverses of Block Matrices -- 3.8 Group Inverses of Companion Matrices Over a Ring -- 3.9 EP Elements -- 4 Drazin Inverses -- 4.1 Drazin Inverses of Complex Matrices -- 4.2 Drazin Inverses of Elements in Semigroups and Rings -- 4.3 Drazin Invertibility in Two Semigroups of a Ring -- 4.4 Jacobson's Lemma and Cline's Formula for Drazin Inverses -- 4.5 Additive Properties of Drazin Inverses of Elements -- 4.6 Drazin Inverses of Products and Differences of Idempotents -- 4.7 Drazin Inverses of Matrices Over a Ring -- 4.8 The Drazin Inverse of a Sum of Morphisms -- 5 Core Inverses -- 5.1 Core Inverses of Complex Matrices -- 5.2 Core Inverses of Elements in Rings with Involution -- 5.2.1 Equivalent Definitions and Characterizations of Core Inverses -- 5.2.2 Relationship Between Group Invertibility and Core Invertibility -- 5.2.3 Characterizations of Core Inverses by AlgebraicEquations -- 5.3 Characterizations of Core Invertibility by Special Elements -- 5.3.1 Characterizations of Core Invertibility by Hermitian Elements or Projections in a Ring -- 5.3.2 Characterizations of Core Invertibility for a Regular Element by Units in a Ring -- 5.4 The Core Inverse of the Sum of Two Core Invertible Elements -- 5.5 The Core Inverse of a Product paq -- 5.6 Core Inverses of Companion Matrices -- 5.7 The Core Inverse of a Sum of Morphisms -- 6 Pseudo Core Inverses -- 6.1 Core-EP Inverses of Complex Matrices -- 6.2 Pseudo Core Inverses of Elements in Rings with Involution -- 6.3 Additive and Multiplicative Properties -- 6.4 Pseudo Core Inverses of Jacobson Pairs -- 6.5 Pseudo Core Inverses of ab and ba -- 6.6 The Pseudo Core Inverse of a Sum of Morphisms -- 6.7 The Pseudo Core Inverse of a Product -- 6.8 The Pseudo Core Inverse of a Low Triangular Matrix -- References -- Index. |