Convexity and concavity of eigenvalue sums |
| |
Authors: | Elliott H Lieb Heinz Siedentop |
| |
Institution: | (1) Departments of Mathematics and Physics, Princeton University, 08544 Princeton, New Jersey;(2) Department of Mathematics, University of Alabama at Birmingham, 35294 Birmingham, Alabama |
| |
Abstract: | It is well known that (H), the sum of the negative eigenvalues of a Hermitian matrixH, is a concave and increasing function ofH. In contrast to this, we prove that forA nonsingular Hermitian andP positive definite, the functionP![map](/content/v2n2841308j3ww18/xxlarge8614.gif) (AP)= (P
1/2
AP
1/2) is convex and decreasing. Several other results of this nature are also proved. |
| |
Keywords: | Convexity concavity eigenvalues |
本文献已被 SpringerLink 等数据库收录! |
|