M-矩阵Fan积特征值界的不等式
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摘要
M-矩阵在数学物理、控制论、电力系统理论等领域有广泛的应用。M-矩阵的Fan积是矩阵分析理论研究中的重要问题。在H9lder不等式的基础上,利用相似矩阵具有相同特征值这一特点给出2个n阶M-矩阵A和B的Fan积AB的最小特征值下界。所得结果只依赖于2个M-矩阵的元素,便于计算。数值算例表明,新估计式在一定条件下改进了现有的一些结果。
M-matrices are applied widely in mathematical physics,cybernetics,electric system and so on.The Fan product of Mmatrices is an important problem in the matrices analysis theories.Based on the H9 lder inequality,lower bounds on the minimum eigenvalue for the Fan product of M-matrices Aand Bare given,since the similar matrices have same eigenvalues.The new bounds only depend on the entries of M-matrices.Therefore,they are easy to calculate.Numerical examples showed that the new bounds improved several existing results.
M-matrices are applied widely in mathematical physics,cybernetics,electric system and so on.The Fan product of Mmatrices is an important problem in the matrices analysis theories.Based on the H9 lder inequality,lower bounds on the minimum eigenvalue for the Fan product of M-matrices Aand Bare given,since the similar matrices have same eigenvalues.The new bounds only depend on the entries of M-matrices.Therefore,they are easy to calculate.Numerical examples showed that the new bounds improved several existing results.
引文
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[5]FANG Maozhong.Bounds on eigenvalues of Hadamard product and the Fan product of matrices[J].Linear Algebra and its Applications,2007,425:7-15.
[6]LI Yaotang,LI Yanyan,WANG Ruiwu,et al.Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices[J].Linear Algebra and its Applications,2010,432:536-545.
[7]GUO Qianping,LI Houbiao,SONG Mingyan.New inequalities on eigenvalues of the Hadamard product and the Fan product of matrices[J].Journal of Inequalities and Applications,2013,2013:433-443.
[8]王峰.矩阵的Hadamard积和Fan积的特征值界的新估计[J].广西师范大学学报(自然科学版),2015,33(3):66-70.WANG Feng.New bounds on eigenvalue of the Hadamard product and the Fan product of matrices[J].Journal of Guangxi Normal University(Natural Science Edition),2015,33(3):66-70.(in Chinese)
[9]GAO Dongjie.Matrix inequalities for the Fan product and the Hadamard product of matrices[J].Advance in Linear Algebra&Matrix Theory,2015(5):90-97.
[10]逄明贤.矩阵谱论[M].长春:吉林大学出版社,1989.PANG Mingxian.Theory of matrix spectrum[M].Changchun:Jilin University Press,1989.(in Chinese)
[2]SHIVAKUMAR P N,WILLIAMS J J,YE Qiang,et al.On two-side bounds related to weakly diagonally dominant M-matrices with applications to digital circuit dynamics[J].SIAM Journal on Matrix Analysis and Applications,1996,17:298-312.
[3]陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2000.CHEN Jingliang,CHEN Xianghui.Special matrices[M].Beijing:Tsinghua University Press,2000.(in Chinese)
[4]HORN R A,JOHNSON C R.Topics in matrix analysis[M].New York:Cambridge University Press,1991.
[5]FANG Maozhong.Bounds on eigenvalues of Hadamard product and the Fan product of matrices[J].Linear Algebra and its Applications,2007,425:7-15.
[6]LI Yaotang,LI Yanyan,WANG Ruiwu,et al.Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices[J].Linear Algebra and its Applications,2010,432:536-545.
[7]GUO Qianping,LI Houbiao,SONG Mingyan.New inequalities on eigenvalues of the Hadamard product and the Fan product of matrices[J].Journal of Inequalities and Applications,2013,2013:433-443.
[8]王峰.矩阵的Hadamard积和Fan积的特征值界的新估计[J].广西师范大学学报(自然科学版),2015,33(3):66-70.WANG Feng.New bounds on eigenvalue of the Hadamard product and the Fan product of matrices[J].Journal of Guangxi Normal University(Natural Science Edition),2015,33(3):66-70.(in Chinese)
[9]GAO Dongjie.Matrix inequalities for the Fan product and the Hadamard product of matrices[J].Advance in Linear Algebra&Matrix Theory,2015(5):90-97.
[10]逄明贤.矩阵谱论[M].长春:吉林大学出版社,1989.PANG Mingxian.Theory of matrix spectrum[M].Changchun:Jilin University Press,1989.(in Chinese)