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Some functions f : R+ → R+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping (JfD) −1 : Mn → Mn on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of (JfD) −1 in the case of a few concrete funct...
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Let M = [ttUiSi /_i be completely nonnegative (CNN), i.e., every minor of Mis nonnegative. Two methods for reducing the eigenvalue problem for M to that of a CNN, tridiagonal matrix, T = [?,-,] (r,-,= 0 when |i — j\ > 1), are presented in this paper. In the particular case that M is nonsingular it is shown for one of the methods that there exists a CNN nonsingular 5 such that SM = TS.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00611-6