Inverse M-matrix inequalities and generalized ultrametric matrices

We prove that the class of GUM matrices is the largest class of bi-potential matrices stable under Hadamard increasing functions. We also show that any power α ≥ 1, in the sense of Hadamard functions, of an inverse M -matrix is also inverse Mmatrix showing a conjecture stated in Neumann [15]. We study the class of filtered matrices, which include naturally the GUM matrices, and present some sufficient conditions for a filtered matrix to be a bi-potential.

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“…In the next Theorem we summarize the main results in [11] and [14] concerning GUM matrices. Theorem 1.1 Let U be a nonnegative matrix.…”

Section: Definition 14 a Nonnegative Matrix U Of Size N Is Said To mentioning

confidence: 98%

“…We recall the following two definitions introduced in [11] and [14], that generalize the concept of ultrametric matrices introduced in [10] (see also [13]). …”

Section: )mentioning

confidence: 99%

Hadamard Functions of Inverse M-Matrices

Dellacherie

Martı́nez

Martı́n

2014

Lecture Notes in Mathematics

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“…By Lemma 4.1 [10], there exists a permutation matrix P such that P AP t is a special NBF. Hence (ii) follows from Lemma 2.2.…”

Section: Special Generalized Ultrametric Matricesmentioning

confidence: 97%

“…Now we assume that A does not contain a row of zeros. By Theorem 4.4 in [10], there exist two rows of A, say p-th and q-th rows for p < q, which are the same. So a pj = a qj for j = 1, .…”

Section: Special Generalized Ultrametric Matricesmentioning

confidence: 99%