By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,respectively.If the characteristic polynomial of the singular...By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,respectively.If the characteristic polynomial of the singular matrix A,p A(s)=det(s E n-A)=s n+a n-1 s n-1+…+a 1 s,is given,then f A(A)=0 and f A(A d,+)=0 in which f A(A)=a 1 x n+a 2 x n-1+…+a n-1 x 2+x,and A and A d,+are the core-EP inverse and the DMP inverse of A,respectively.Furthermore,some properties of the characteristic polynomials of A D∈C n,n and A∈C n,n are derived.展开更多
We study the constrained systemof linear equations Ax=b,x∈R(A^(k))for A∈C^(n×n)and b∈Cn,k=Ind(A).When the system is consistent,it is well known that it has a unique A^(D)b.If the system is inconsistent,then we...We study the constrained systemof linear equations Ax=b,x∈R(A^(k))for A∈C^(n×n)and b∈Cn,k=Ind(A).When the system is consistent,it is well known that it has a unique A^(D)b.If the system is inconsistent,then we seek for the least squares solution of the problem and consider min_(x∈R(A^(k)))||b−Ax||2,where||·||2 is the 2-norm.For the inconsistent system with a matrix A of index one,it was proved recently that the solution is A^(■)b using the core inverse A^(■)of A.For matrices of an arbitrary index and an arbitrary b,we show that the solution of the constrained system can be expressed as A^(■)b where A^(■)is the core-EP inverse of A.We establish two Cramer’s rules for the inconsistent constrained least squares solution and develop several explicit expressions for the core-EP inverse of matrices of an arbitrary index.Using these expressions,two Cramer’s rules and one Gaussian elimination method for computing the core-EP inverse of matrices of an arbitrary index are proposed in this paper.We also consider the W-weighted core-EP inverse of a rectangular matrix and apply the weighted core-EP inverse to a more general constrained system of linear equations.展开更多
We study a new binary relation defined on the set of rectangular complex matrices involving the weighted core-EP inverse and give its characterizations.This relation becomes a pre-order.Then,one-sided preorders associ...We study a new binary relation defined on the set of rectangular complex matrices involving the weighted core-EP inverse and give its characterizations.This relation becomes a pre-order.Then,one-sided preorders associated to the weighted core-EP inverse are given from two perspectives.Finally,we make a comparison for these two sets of one-sided weighted pre-orders.展开更多
In this paper,we study the displacement rank of the Core-EP inverse.Both Sylvester displacement and generalized displacement are discussed.We present upper bounds for the ranks of the displacements of the Core-EP inve...In this paper,we study the displacement rank of the Core-EP inverse.Both Sylvester displacement and generalized displacement are discussed.We present upper bounds for the ranks of the displacements of the Core-EP inverse.Numerical experiments are presented to demonstrate the efficiency and accuracy.展开更多
We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recentl...We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073- 3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in *-rings.展开更多
This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin...This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin inverses established by R.E.Cline.The result is then extended to the core-EP inverses.展开更多
基金The China Postdoctoral Science Foundation(No.2015M581690)the National Natural Science Foundation of China(No.11371089)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20141327)the Special Fund for Bagui Scholars of Guangxi
文摘By using the classical Cayley-Hamilton theorem,the polynomial equations of the core-EP inverse matrix and Drazin-Moore-Penrose(DMP)inverse matrix are given,respectively.If the characteristic polynomial of the singular matrix A,p A(s)=det(s E n-A)=s n+a n-1 s n-1+…+a 1 s,is given,then f A(A)=0 and f A(A d,+)=0 in which f A(A)=a 1 x n+a 2 x n-1+…+a n-1 x 2+x,and A and A d,+are the core-EP inverse and the DMP inverse of A,respectively.Furthermore,some properties of the characteristic polynomials of A D∈C n,n and A∈C n,n are derived.
文摘We study the constrained systemof linear equations Ax=b,x∈R(A^(k))for A∈C^(n×n)and b∈Cn,k=Ind(A).When the system is consistent,it is well known that it has a unique A^(D)b.If the system is inconsistent,then we seek for the least squares solution of the problem and consider min_(x∈R(A^(k)))||b−Ax||2,where||·||2 is the 2-norm.For the inconsistent system with a matrix A of index one,it was proved recently that the solution is A^(■)b using the core inverse A^(■)of A.For matrices of an arbitrary index and an arbitrary b,we show that the solution of the constrained system can be expressed as A^(■)b where A^(■)is the core-EP inverse of A.We establish two Cramer’s rules for the inconsistent constrained least squares solution and develop several explicit expressions for the core-EP inverse of matrices of an arbitrary index.Using these expressions,two Cramer’s rules and one Gaussian elimination method for computing the core-EP inverse of matrices of an arbitrary index are proposed in this paper.We also consider the W-weighted core-EP inverse of a rectangular matrix and apply the weighted core-EP inverse to a more general constrained system of linear equations.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11771076)sponsored by Shanghai Sailing Program(Grant No.20YF1433100).
文摘We study a new binary relation defined on the set of rectangular complex matrices involving the weighted core-EP inverse and give its characterizations.This relation becomes a pre-order.Then,one-sided preorders associated to the weighted core-EP inverse are given from two perspectives.Finally,we make a comparison for these two sets of one-sided weighted pre-orders.
基金Supported by Guangxi Natural Science Foundation(2018GXNSFDA281023,2018GXNSFAA138181)High Level Innovation Teams and Distinguished Scholars in Guangxi Universities(GUIJIAOREN201642HAO)+3 种基金Graduate Research Innovation Project of Guangxi University for Nationalities(gxun-chxzs2018041,gxun-chxzs2019026)the Special Fund for Bagui Scholars of Guangxi(2016A17)the National Natural Science Foundation of China(61772006,12061015)the Science and Technology Major Project of Guangxi(AA17204096)。
文摘In this paper,we study the displacement rank of the Core-EP inverse.Both Sylvester displacement and generalized displacement are discussed.We present upper bounds for the ranks of the displacements of the Core-EP inverse.Numerical experiments are presented to demonstrate the efficiency and accuracy.
文摘We study properties of a relation in *-rings, called the core-EP (pre)order which was introduced by H. Wang on the set of all n × n complex matrices [Linear Algebra Appl., 2016, 508: 289-300] and has been recently generalized by Y. Gao, J. Chen, and Y. Ke to *-rings [Filomat, 2018, 32: 3073- 3085]. We present new characterizations of the core-EP order in *-rings with identity and introduce the notions of the dual core-EP decomposition and the dual core-EP order in *-rings.
文摘This paper presents a formula for the Drazin inverses of matrices based on a sequence of partial full-rank factorizations which theoretically extends the classic full-rank factorization method for computing the Drazin inverses established by R.E.Cline.The result is then extended to the core-EP inverses.
