We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a Banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the gen...We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a Banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix. Also, several particular cases of this result are considered.展开更多
We present the weighted weak group inverse,which is a new generalized inverse of operators between two Hilbert spaces,and we extend the notation of the weighted weak group inverse for rectangular matrices.Some charact...We present the weighted weak group inverse,which is a new generalized inverse of operators between two Hilbert spaces,and we extend the notation of the weighted weak group inverse for rectangular matrices.Some characterizations and representations of the weighted weak group inverse are investigated.We also apply these results to define and study the weak group inverse for a Hilbert space operator.Using the weak group inverse,we define and characterize various binary relations.展开更多
Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element,the authors answer in this paper. Several new ch...Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element,the authors answer in this paper. Several new characterizations of star-core, normal and Hermitian elements in R are also presented.展开更多
In this paper,we mainly give characterizations of EP elements in terms of equations.In addition,a related notion named a central EP element is defined and investigated.Finally,we focus on characterizations of a genera...In this paper,we mainly give characterizations of EP elements in terms of equations.In addition,a related notion named a central EP element is defined and investigated.Finally,we focus on characterizations of a generalized EP element,i.e.,+-DMP element.展开更多
The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses.As a significant application of the Moore-Penrose inverse,the best approximation solution to linea...The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses.As a significant application of the Moore-Penrose inverse,the best approximation solution to linear matrix equations(i.e.both least squares and the minimal norm)is considered.Also,characterizations of least squares solution and solution of minimum norm are given.Basic properties of the Drazin-inverse solution and the outer-inverse solution are present.Motivated by recent research,important least square properties of composite outer inverses are collected.展开更多
基金supported by the Ministry of Education and Science,Republic of Serbia(174007)
文摘We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a Banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix. Also, several particular cases of this result are considered.
基金The first author was supported by the Ministry of Education,Science and Technological Development,Republic of Serbia,Grant No.174007(451-03-68/2020-14/200124)The second author was supported by the National Natural Science Foundation of China(Grant Nos.11901079,61672149,11601211)the Scientific and Technological Research Program Foundation of Jilin Province,China(Grant Nos.JJKH20190690KJ,20190201095JC,20200401085GX.)。
文摘We present the weighted weak group inverse,which is a new generalized inverse of operators between two Hilbert spaces,and we extend the notation of the weighted weak group inverse for rectangular matrices.Some characterizations and representations of the weighted weak group inverse are investigated.We also apply these results to define and study the weak group inverse for a Hilbert space operator.Using the weak group inverse,we define and characterize various binary relations.
基金supported by the National Natural Science Foundation of China(Nos.11201063,11771076)the Ministry of Education and Science,Republic of Serbia(No.174007)
文摘Let R be a ring with involution. It is well-known that an EP element in R is a core invertible element, but the question when a core invertible element is an EP element,the authors answer in this paper. Several new characterizations of star-core, normal and Hermitian elements in R are also presented.
基金The research was supported by the Ministry of Education,Science and Technological Development(grant no.174007)Republic of Serbia,and by NSF of China(11901510)+1 种基金NSF of Jiangsu Province of China(BK20170589)China Postdoctoral Science Foundation Funded Project(2017M611920).
文摘In this paper,we mainly give characterizations of EP elements in terms of equations.In addition,a related notion named a central EP element is defined and investigated.Finally,we focus on characterizations of a generalized EP element,i.e.,+-DMP element.
基金P.S.Stanimirovic was supported by the Ministry of Education and Science,Republic of Serbia(Grant 174013/451-03-9/2021-14/200124)D.Mosic was supported by the Ministry of Education,Science and Technological Development,Republic of Serbia(Grant 174007/451-03-9/2021-14/200124)Y.Wei was supported by the bilateral project between China and Serbia The theory of tensors,operator matrices and applications(no.4-5)'.
文摘The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses.As a significant application of the Moore-Penrose inverse,the best approximation solution to linear matrix equations(i.e.both least squares and the minimal norm)is considered.Also,characterizations of least squares solution and solution of minimum norm are given.Basic properties of the Drazin-inverse solution and the outer-inverse solution are present.Motivated by recent research,important least square properties of composite outer inverses are collected.
