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1.
Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse are given. These bounds improve the results of [H.B. Li, T.Z. Huang, S.Q. Shen, H. Li, Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse, Linear Algebra Appl. 420 (2007) 235-247].  相似文献   

2.
We show that for any pair M,N of n by n M-matrices, the Hadamard (entry-wise) product M°N -1 is again an M-matrix. For a single M-matrix M, the matrix M°M -1 is also considered.  相似文献   

3.
Some new bounds on the spectral radius of matrices   总被引:2,自引:0,他引:2  
A new lower bound on the smallest eigenvalue τ(AB) for the Fan product of two nonsingular M-matrices A and B is given. Meanwhile, we also obtain a new upper bound on the spectral radius ρ(A°B) for nonnegative matrices A and B. These bounds improve some results of Huang (2008) [R. Huang, Some inequalities for the Hadamard product and the Fan product of matrices, Linear Algebra Appl. 428 (2008) 1551-1559].  相似文献   

4.
Some inequalities for the Hadamard product and the Fan product of matrices   总被引:2,自引:0,他引:2  
If A and B are nonsingular M-matrices, a sharp lower bound on the smallest eigenvalue τ(AB) for the Fan product of A and B is given, and a sharp lower bound on τ(A°B-1) for the Hadamard product of A and B-1 is derived. In addition, we also give a sharp upper bound on the spectral radius ρ(A°B) for nonnegative matrices A and B.  相似文献   

5.
A well-known property of an M-matrix M is that the inverse is element-wise non-negative, which we write as M-1?0. In this paper, we consider element-wise perturbations of non-symmetric tridiagonal M-matrices and obtain sufficient bounds on the perturbations so that the non-negative inverse persists. These bounds improve the bounds recently given by Kennedy and Haynes [Inverse positivity of perturbed tridiagonal M-matrices, Linear Algebra Appl. 430 (2009) 2312-2323]. In particular, when perturbing the second diagonals (elements (l,l+2) and (l,l-2)) of M, these sufficient bounds are shown to be the actual maximum allowable perturbations. Numerical examples are given to demonstrate the effectiveness of our estimates.  相似文献   

6.
Let Mn be the space of all n × n complex matrices, and let Γn be the subset of Mn consisting of all n × n k-potent matrices. We denote by Ψn the set of all maps on Mn satisfying A − λB ∈ Γn if and only if ?(A) − λ?(B) ∈ Γn for every A,B ∈ Mn and λ ∈ C. It was shown that ? ∈ Ψn if and only if there exist an invertible matrix P ∈ Mn and c ∈ C with ck−1 = 1 such that either ?(A) = cPAP−1 for every A ∈ Mn, or ?(A) = cPATP−1 for every A ∈ Mn.  相似文献   

7.
We prove an inequality for the spectral radius of products of non-negative matrices conjectured by X. Zhan. We show that for all n×n non-negative matrices A and B, ρ(A°B)?ρ((A°A)(B°B))1/2?ρ(AB), in which ° represents the Hadamard product.  相似文献   

8.
Let F(A) be the numerical range or the numerical radius of a square matrix A. Denote by A ° B the Schur product of two matrices A and B. Characterizations are given for mappings on square matrices satisfying F(A ° B) = F(?(A) ° ?(B)) for all matrices A and B. Analogous results are obtained for mappings on Hermitian matrices.  相似文献   

9.
Let A1, … , Ak be positive semidefinite matrices and B1, … , Bk arbitrary complex matrices of order n. We show that
span{(A1x)°(A2x)°?°(Akx)|xCn}=range(A1°A2°?°Ak)  相似文献   

10.
Let b = b(A) be the Boolean rank of an n × n primitive Boolean matrix A and exp(A) be the exponent of A. Then exp(A) ? (b − 1)2 + 2, and the matrices for which equality occurs have been determined in [D.A. Gregory, S.J. Kirkland, N.J. Pullman, A bound on the exponent of a primitive matrix using Boolean rank, Linear Algebra Appl. 217 (1995) 101-116]. In this paper, we show that for each 3 ? b ? n − 1, there are n × n primitive Boolean matrices A with b(A) = b such that exp(A) = (b − 1)2 + 1, and we explicitly describe all such matrices.  相似文献   

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