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Principal pivot transforms: properties and applications
The principal pivot transform (PPT) is a transformation of the matrix of a linear system tantamount to exchanging unknowns with the corresponding entries of the right-hand side of the system. TheExpand
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Generating and detecting matrices with positive principal minors
A brief but concise review of methods to generate P-matrices (i.e., matrices having positive principal minors) is provided and motivated by open problems on P-matrices and the desire to develop andExpand
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Ray patterns of matrices and nonsingularity
A complex matrix A is ray-nonsingular if det(X 0 A) f 0 for every matrix X with positive entries. A sufficient condition for ray nonsingularity is that the origin is not in the relative interior ofExpand
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Sign patterns that allow eventual positivity
Several necessary or sufficient conditions for a sign patternto allow eventual posi- tivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity.Expand
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Reachability and Holdability of Nonnegative States
TLDR
Linear differential systems $\dot{x}(t)=Ax(t)$ ($A\in\mathbb{R}^{n\times n}$, $x_0=x(0) in finite time$, $t\geq0$) whose solutions become and remain nonnegative are studied. Expand
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Inverse M-Matrix Inequalities and Generalized Ultrametric Matrices
Abstract We use weighted directed graphs to introduce a class of nonnegative matrices which, under a simple condition, are inverse M-matrices. We call our class the generalized ultrametic matrices,Expand
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Inverses of Unipathic M-Matrices
TLDR
In this paper we characterize all nonnegative matrices whose inverses are M-matrices with unipathic digraphs. Expand
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SIGN PATTERNS THAT REQUIRE EVENTUAL POSITIVITY OR REQUIRE EVENTUAL NONNEGATIVITY
It is shown that a square sign pattern A requires eventual positivity if and only if it is nonnegative and primitive. Let the set of vertices in the digraph of A that have access to a vertex s beExpand
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Noncirculant Toeplitz matrices all of whose powers are Toeplitz
Let a, b and c be fixed complex numbers. Let Mn(a, b, c) be the n × n Toeplitz matrix all of whose entries above the diagonal are a, all of whose entries below the diagonal are b, and all of whoseExpand
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Convex sets of nonsingular and P:–Matrices
We show that the set r(A,B) (resp. c(A,B)) of square matrices whose rows (resp. columns) are independent convex combinations of
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