In terms of Hadamard product, a new model is proposed for the control of connection coefficients of the state variables of the systems. The control law to stabilize the systems via the regulations of connection coeffi...In terms of Hadamard product, a new model is proposed for the control of connection coefficients of the state variables of the systems. The control law to stabilize the systems via the regulations of connection coefficients is obtained via a Hadamard product involved bilinear matrix inequalities. This new control model may be of significant applications in many fields, especially may be of some special sense in the emergency control such as isolation and obstruction control.展开更多
Suppose that A and B are two positive-definite matrices,then,the limit of(A^p/2B^pA^p/2)1/p as p tends to 0 can be obtained by the well known Lie-Trotter formula.In this article,we generalize the usual product of matr...Suppose that A and B are two positive-definite matrices,then,the limit of(A^p/2B^pA^p/2)1/p as p tends to 0 can be obtained by the well known Lie-Trotter formula.In this article,we generalize the usual product of matrices to the Hadamard product denoted as*which is commutative,and obtain the explicit formula of the limit(A^p*B^p)^1/p as p tends to 0.Furthermore,the existence of the limit of(A^p*B^p)^1/p as p tends to+∞is proved.展开更多
1 IntroductionFor an n×n matrix A which is an inverse M-matrix,M.Neumann in [1]conjecturedthat the Hadamard product A·A is an inverse of an M-matrix.They have checked hisconjecture without failure on Ultrame...1 IntroductionFor an n×n matrix A which is an inverse M-matrix,M.Neumann in [1]conjecturedthat the Hadamard product A·A is an inverse of an M-matrix.They have checked hisconjecture without failure on Ultrametric matrices and inverse of MMA-matrices,Uni-pathicmatrices and the Willongby inverse M-matrices.Bo-Ying Wang et al.in[2]haveinvestigated Triangular inverse M-matrices which are closed under the Hadamard multipli-cation.Lu Linzheng,Sun Weiwei and Li Wen in[3]presented a more general展开更多
In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard ...In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.展开更多
A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained....A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.展开更多
In this paper, some estimations of bounds for determinant of Hadamard product of H-matrices are given. The main result is the following: if A= (aij) and B=(bij) are nonsingular H-matrices of order n and ∏in=1, aiibii...In this paper, some estimations of bounds for determinant of Hadamard product of H-matrices are given. The main result is the following: if A= (aij) and B=(bij) are nonsingular H-matrices of order n and ∏in=1, aiibii> 0, and Ak and Bk, k = 1, 2,…,n, are the k× k leading principal submatrices of A and B, respectively, then where M(Ak) denotes the comparison mains of Ak.展开更多
In this paper, some new results on the estimations of bounds for determinant of Hadamard Product of two H-matrices are given. Several recent results are improved and generalized.
For the Hadamard product of an M-matrix and its inverse, some new lower bounds on the minimum eigenvalue are given. These bounds can improve considerably some previous results.
In this paper,we establish some Brauer-type bounds for the spectral radius of Hadamard product of two nonnegative tensors based on Brauer-type inclusion set,which are shown to be sharper than the existing bounds estab...In this paper,we establish some Brauer-type bounds for the spectral radius of Hadamard product of two nonnegative tensors based on Brauer-type inclusion set,which are shown to be sharper than the existing bounds established in the literature.The validity of the obtained results is theoretically and numerically tested.展开更多
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
基金supported by the National Natural Science Foundation of China (No.60874007)the Research Fund for the Doctoral Program of Higher Education (No.200802550024)
文摘In terms of Hadamard product, a new model is proposed for the control of connection coefficients of the state variables of the systems. The control law to stabilize the systems via the regulations of connection coefficients is obtained via a Hadamard product involved bilinear matrix inequalities. This new control model may be of significant applications in many fields, especially may be of some special sense in the emergency control such as isolation and obstruction control.
基金H.Sun is supported by NSFC(61179031)J.Wang is supported by General Project of Science and Technology Plan of Beijing Municipal Education Commission(KM202010037003).
文摘Suppose that A and B are two positive-definite matrices,then,the limit of(A^p/2B^pA^p/2)1/p as p tends to 0 can be obtained by the well known Lie-Trotter formula.In this article,we generalize the usual product of matrices to the Hadamard product denoted as*which is commutative,and obtain the explicit formula of the limit(A^p*B^p)^1/p as p tends to 0.Furthermore,the existence of the limit of(A^p*B^p)^1/p as p tends to+∞is proved.
文摘1 IntroductionFor an n×n matrix A which is an inverse M-matrix,M.Neumann in [1]conjecturedthat the Hadamard product A·A is an inverse of an M-matrix.They have checked hisconjecture without failure on Ultrametric matrices and inverse of MMA-matrices,Uni-pathicmatrices and the Willongby inverse M-matrices.Bo-Ying Wang et al.in[2]haveinvestigated Triangular inverse M-matrices which are closed under the Hadamard multipli-cation.Lu Linzheng,Sun Weiwei and Li Wen in[3]presented a more general
文摘In this paper, we present the general exact solutions of such coupled system of matrix fractional differential equations for diagonal unknown matrices in Caputo sense by using vector extraction operators and Hadamard product. Some illustrated examples are also given to show our new approach.
文摘A new inequality on the minimum eigenvalue for the Fan product of nonsingular M-matrices is given. In addition, a new inequality on the spectral radius of the Hadamard product of nonnegative matrices is also obtained. These inequalities can improve considerably some previous results.
基金This work is supported by the Science Foundations of Yunnan Province (2000A0001-1M) and the ScienceFoundations of the Eduation
文摘In this paper, some estimations of bounds for determinant of Hadamard product of H-matrices are given. The main result is the following: if A= (aij) and B=(bij) are nonsingular H-matrices of order n and ∏in=1, aiibii> 0, and Ak and Bk, k = 1, 2,…,n, are the k× k leading principal submatrices of A and B, respectively, then where M(Ak) denotes the comparison mains of Ak.
基金This work is supported by the Science Foundations of the Education Department of Yunnan Province （03Z169A） and the Science Foundations of Yunnan University （2003Z013C）.
文摘In this paper, some new results on the estimations of bounds for determinant of Hadamard Product of two H-matrices are given. Several recent results are improved and generalized.
基金Supported by National Natural Science Foundations of China(11361074,11501141,11601473)CAS ’Light of West China’ Program
文摘For the Hadamard product of an M-matrix and its inverse, some new lower bounds on the minimum eigenvalue are given. These bounds can improve considerably some previous results.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11671228).
文摘In this paper,we establish some Brauer-type bounds for the spectral radius of Hadamard product of two nonnegative tensors based on Brauer-type inclusion set,which are shown to be sharper than the existing bounds established in the literature.The validity of the obtained results is theoretically and numerically tested.
文摘We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
基金Supported by National Natural Science Foundation of China(11271045)Research Fund for the Doctoral Program of China(20100003110004)+1 种基金Natural Science Foundation of Inner Mongolia(2010MS0117)Higher School Foundation of Inner Mongolia(NJzc08160)
