Convexity and concavity of eigenvalue sums |
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| Authors: | Elliott H Lieb Heinz Siedentop |
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| 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 |
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| 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 (AP)=(P
1/2
AP
1/2) is convex and decreasing. Several other results of this nature are also proved. |
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| Keywords: | Convexity concavity eigenvalues |
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