On Brauer-Ostrowski and Brualdi sets
On Brauer-Ostrowski and Brualdi sets
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DOI：
10.1016/j.laa.2014.02.029
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发表时间：
2014-05
影响因子：
1.1
通讯作者：
A. Hadjidimos;M. Tzoumas
中科院分区：
文献类型：
--
作者：
A. Hadjidimos;M. Tzoumas
对于复方阵特征值谱的局部化问题，Ostrowski利用矩阵行和、列和的广义几何平均，推广了经典的Geršgorin定理。Ostrowski和Brauer通过使用两个行和列和的乘积的广义几何平均值扩展了以前的想法。最后，Brualdi利用图论，通过考虑两个或两个以上的行和列和的乘积的广义几何平均值，进一步扩展了以前的所有思想。这些局部化结果还可以提供非奇异矩阵的类别。本文的主要目的是利用上述所有已知的结果，并确定所涉及的参数α（α k's）的区间，从而使所讨论的谱的局部化以及相应的非奇异矩阵类的确定成为可能。
For the localization of the spectrum of the eigenvalues of a complex square matrix, the classical Geršgorin Theorem was extended by Ostrowski who used the generalized geometric mean of the row and column sums of the matrix. Ostrowski, and Brauer, extended the previous idea by using generalized geometric means of products of two row and column sums. Finally, by using the Graph Theory, Brualdi extended all of the previous ideas further by considering generalized geometric means of products of two or more than two row and column sums. These localization results can also provide classes of nonsingular matrices. Our main aim in this work is to exploit all the above known results and determine intervals for the parameter (s) α (α k's) involved so that the localization of the spectrum in question as well as the determination of the associated class of nonsingular matrices are possible.