We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators le...We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville's inclusions are made into equalities.展开更多
We investigate relationships between the Moore-Penrose inverse （ABA^＊）＋ and the product [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） through some rank and inertia formulas for the difference of （ABA^＊）^＋ - [（AB）^...We investigate relationships between the Moore-Penrose inverse （ABA^＊）＋ and the product [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） through some rank and inertia formulas for the difference of （ABA^＊）^＋ - [（AB）^（1,2,3）]^＊B（AB）^（1,2,3）, where B is Hermitian matrix and （AB）^（1,2,3） is a {1, 2, 3}-inverse of AB. We show that there always exists an （AB）^（1,2,3） such that （ABA^＊）^＋ = [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） holds. In addition, we also establish necessary and sufficient conditions for the two inequalities （ABA^＊）^＋ 〉 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） and （ABA^＊）^＋〈4 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） to hold in the LSwner partial ordering. Some variations of the equalities and inequalities are also presented. In particular, some equalities and inequalities for the Moore-Penrose inverse of the sum A ＋ B of two Hermitian matrices A and B are established.展开更多
基金This work has been financially supported by the research deputy of education and Research University of Torbat Heydarieh,the grant number is UTH:1399/8/2483。
文摘We establish new identities for Moore-Penrose inverses of some operator products,and prove their associated reverse-order laws.Moreover,our results concerning the Moore-Penrose inverse of a product of two operators lead in finding a relation between the operators in the case where Greville's inclusions are made into equalities.
基金Supported by the National Natural Science Foundation of China(Grant No.11271384)
文摘We investigate relationships between the Moore-Penrose inverse （ABA^＊）＋ and the product [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） through some rank and inertia formulas for the difference of （ABA^＊）^＋ - [（AB）^（1,2,3）]^＊B（AB）^（1,2,3）, where B is Hermitian matrix and （AB）^（1,2,3） is a {1, 2, 3}-inverse of AB. We show that there always exists an （AB）^（1,2,3） such that （ABA^＊）^＋ = [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） holds. In addition, we also establish necessary and sufficient conditions for the two inequalities （ABA^＊）^＋ 〉 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） and （ABA^＊）^＋〈4 [（AB）^（1,2,3）]^＊B（AB）^（1,2,3） to hold in the LSwner partial ordering. Some variations of the equalities and inequalities are also presented. In particular, some equalities and inequalities for the Moore-Penrose inverse of the sum A ＋ B of two Hermitian matrices A and B are established.
