非负中心对称矩阵的扰动特征值
Perturbing eigenvalues of nonnegative centrosymmetric matrices
摘要：
一个$n\times n$矩阵$C$被称为{ \it中心对称}，如果它满足关系$JCJ=C$，其中$J$是$n\times n$反同一性矩阵。中心对称矩阵具有丰富的特征结构，在文献中已经得到了广泛的研究。中心对称矩阵的许多结果已经被推广到更广泛的矩阵类，出现在各种各样的学科。本文研究了非负中心对称矩阵的谱性质。我们展示了如何改变一个单一的特征值，两个或三个特征值的$n\times n$非负中心对称矩阵，而不改变任何其余的特征值既不非负性，也不中心对称结构。此外，我们的结果还部分地回答了郭[11]和郭和郭[12]提出的一些已知问题.我们的证明生成算法程序，允许计算一个解决方案矩阵。
英文摘要：
An $n\times n$ matrix $C$ is said to be {\it centrosymmetric} if it satisfies the relation $JCJ=C$, where $J$ is the $n\times n$ counteridentity matrix. Centrosymmetric matrices have a rich eigenstructure that has been studied extensively in the literature. Many results for centrosymmetric matrices have been generalized to wider classes of matrices that arise in a wide variety of disciplines. In this paper, we obtain interesting spectral properties for nonnegative centrosymmetric matrices. We show how to change one single eigenvalue, two or three eigenvalues of an $n\times n$ nonnegative centrosymmetric matrix without changing any of the remaining eigenvalues neither nonnegativity nor the centrosymmetric structure. Moreover, our results allow partially answer some known questions given by Guo [11] and by Guo and Guo [12]. Our proofs generate algorithmic procedures that allow to compute a solution matrix.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
