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
In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new...In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L*partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.展开更多
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.
基金The work was supported by the Research Fund Project of Guangxi University for Nationalities(No.2019KJQD03)Guangxi Natural Science Foundation(No.2018GXNSFDA281023)+2 种基金the National Natural Science Foundation of China(No.12061015)the Special Fund for Bagui Scholars of Guangxi(No.2016A17)the Education Innovation Program for 2019 Graduate Students(No.gxun-chxzs 2019026).
文摘In this paper,we use the Lowner partial order and the star partial order to introduce a new partial order(denoted by"L^(*)")on the set of group matrices,and get some characteristics and properties of the new partial order.In particular,we prove that the L*partial order is a special kind of the core partial order and it is equivalent to the star partial order under some conditions.We also illustrate its difference from other partial orders with examples and find out under what conditions it is equivalent to other partial orders.
