Convexity and log convexity for the spectral radius
نویسندگان
چکیده
منابع مشابه
Convexity and Log Convexity for the Spectral Radius
The starting point of this paper is a theorem by J. F. C. Kingman which asserts that if the entries of a nonnegative matrix are log convex functions of a variable then so is the spectral radius of the matrix. A related result of J. Cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements. The first section of this paper gives a new, unified pr...
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Friedland (1981) showed that for a nonnegative square matrix A, the spectral radius r(eA) is a log-convex functional over the real diagonal matrices D. He showed that for fully indecomposable A, log r(eA) is strictly convex over D1,D2 if and only if D1 −D2 6= c I for any c ∈ R. Here the condition of full indecomposability is shown to be replaceable by the weaker condition that A and A>A be irre...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1986
ISSN: 0024-3795
DOI: 10.1016/0024-3795(86)90233-8