论文标题
矩阵特征值的包含区域和界限
Inclusion regions and bounds for the eigenvalues of matrices with a known eigenpair
论文作者
论文摘要
令（λ，v）为正方形的真实矩阵A的已知真实特征。在本文中，它显示了如何根据v。v。所获得的区域的组件来定位A的其他特征值。两种情况是 根据V的某些组件是否等于零。以两种不同的方式获得上限，以除λ以外的其他绝对值，以最大的特征值获得。提供了详细的示例。尽管有些强调了非负不可约的矩阵，但本文的主要结果对于任何正方形的真实矩阵都是有效的。
Let (λ, v) be a known real eigenpair of a square real matrix A. In this paper it is shown how to locate the other eigenvalues of A in terms of the components of v. The obtained region is a union of Gershgorin discs of the second type recently introduced by the authors in a previous paper. Two cases are considered depending on whether or not some of the components of v are equal to zero. Upper bounds are obtained, in two different ways, for the largest eigenvalue in absolute value of A other than λ. Detailed examples are provided. Although nonnegative irreducible matrices are somewhat emphasized, the main results in this paper are valid for any square real matrix.
