约束矩阵谱的曲线和包络
Curves and envelopes that bound the spectrum of a matrix
摘要：
给出了Adam、Psarrakos和Tsatsomeros利用复矩阵A的埃尔米特部分H（A）的最大特征值的知识来寻找复矩阵A的特征值不等式的方法的推广。A的数值范围或数值域可以构造为由H的最大本征值（$e^{iθ}$ A）确定的半平面的交点。Adam，Psarrakos和Tsatsomeros证明了利用H（A）的两个最大特征值，A的特征值满足三次不等式，并且这种三次曲线的包络在复平面上定义了一个小于数值域但仍包含A的谱的区域.本文给出了如何利用H（A）的三个或更多的最大特征值，得到关于A的特征值的新的不等式和包含A的谱的新的S型区域。
英文摘要：
A generalization of the method developed by Adam, Psarrakos and Tsatsomeros to find inequalities for the eigenvalues of a complex matrix A using knowledge of the largest eigenvalues of its Hermitian part H(A) is presented. The numerical range or field of values of A can be constructed as the intersection of half-planes determined by the largest eigenvalue of H($e^{iθ}$A). Adam, Psarrakos and Tsatsomeros showed that using the two largest eigenvalues of H(A), the eigenvalues of A satisfy a cubic inequality and the envelope of such cubic curves defines a region in the complex plane smaller than the numerical range but still containing the spectrum of A. Here it is shown how using the three largest eigenvalues of H(A) or more, one obtains new inequalities for the eigenvalues of A and new envelope-type regions containing the spectrum of A.
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。
