On the extreme eigenvalues of block 2 × 2 Hermitian matrices

被引：0

作者：

Kolotilina L.Y. ^{[1
]}

机构：

[1] St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg

来源：

Journal of Mathematical Sciences | 2005年 / 127卷 / 3期

关键词：

Explicit Expression; Hermitian Matrice; Extreme Eigenvalue; Hermitian Block;

D O I：

10.1007/s10958-005-0155-6

中图分类号：

学科分类号：

摘要：

The lower bound λ1(A) - λn(A)≥ 2∥ A12∥ for the difference of the extreme eigenvalues of an n × n Hermitian block 2 × 2 matrix A = [A11 A 12/A*12A22] is established, and conditions necessary and sufficient for this bound to be attained at A are provided. Some corollaries of this result are derived. In particular, for a positive-definite matrix A, it is demonstrated that λ1 (A) - λn (A) = 2∥A12∥ if and only if A is optimally conditioned, and explicit expressions for the extreme eigenvalues of such matrices are obtained. Bibliography: 5 titles. © 2005 Springer Science+Business Media, Inc.

引用

页码：1969 / 1975

页数：6

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