120901930
Nonnegative jordan bases
In this paper we are concerned with the problem of when the generalized eigenspace of an n × n nonegative matrix A corresponding to its spectrai radius ρ has a nonnegative Jordan basis. Richman and Schneider have shown this to hold when, and only when, the Weyr characteristics of A corresponding to ρ is equal to the vector of levels in the singular graph of A Here we develop sufficient conditions for this equality to hold based upon the linear independence of a certain set of vectors which are generated according to a process of elimination of totally independent chains from the singular graph. We show that this condition comes close to being a further characterization for the existence of a nonnegative Jordan basis for this eigenspace and actually conjecture that this is the case. Finally, we show that this eigenspace has a Rothblum basis which is a Jordan basis if and only if the singular graph is a disjoint union of chains.
121748192
A note on generalizations of strict diagonal dominance for real matrices
Abstract We investigate classes of real square matrices possessing some weakened from of strict diagonal dominance of a real matrix whose diagonal entries are all positive. The intersection of each one of these classes with the set of all real matrices, with nonpositive off-diagonal elements, coincides with the set of all nonsingular M - matrices.
121745003
The Kahan S.O.R. convergence bound for nonsingular and irreducible M-matrices
Abstract Let A be a nonsingular M -matrix, and let π be a block partitioning of A such that the diagonal blocks are square. Denote by J A π and A π ω the block Jacobi and the block S.O.R. iteration matrices arising from and associated with the partitioning π of A , respectively. In [5] Kahan showed that ρ ( A π ω J A π )]. Under the assumption that J A π is irreducible we examine the question of when ρ( A π ω' )=1 for certain recurring M -matrices.
122147649
Cone reachability for linear differential systems
Given a real nxn matrix A and a simplicial cone which is positively invariant under the linear differential system , we consider the problem of characterizing the closure of the set XA(K) of all initial points x(0) ∈ Rn which give rise to solutions x(t) that enter (and remain in) K. An explicit characterization of the closure of XA(K) is given first in case A is diagon-able with a real spectrum. Subsequently a characterization for the closure of XA(K) is given in case there exist k ∈ int K such that −Ak ∈ K, but in the absence of any other explicit assumptions on A.
120746270
On the square roots of strictly quasiaccretive complex matrices
Abstract The square roots of a complex n × n matrix A for which the real part of e ix A , where χϵ[ −π 2 , π 2 ] , is positive definite are investigated. It is shown, for example, that when χ= −π 2 (i.e., A is strictly dissipative), A has a unique square root whose real and imaginary parts are both positive definite.
18512153
Algorithms for Computing Bases for the Perron Eigenspace with PrescribedNonnegativity and Combinatorial Properties
Let $P$ be an $n \times n$ nonnegative matrix. In this paper the authors introduce a method called the SCANBAS algorithm for computing a union of (Jordan) chains $\cal{C}$ corresponding to the Perron eigenvalue of $P$, such that $\cal{C}$ consists of nonnegative vectors only and such that at each height, $\cal{C}$ contains the maximal number of nonnegative vectors of that height possible in a height basis for the Perron eigenspace of $P$. It is further shown that $\cal{C}$ can be extended to a height basis for the Perron eigenspace of $P$. The chains are extracted from transform components of $P$ that are, in turn, polynomials in $P$. When the Perron eigenspace has a Jordan basis consisting of nonnegative vectors only, this algorithm computes such a basis. The paper concludes with various examples computed by the algorithm using MATLAB. The work here continues and deepens work on computing nonnegative bases for the Perron eigenspace from polynomials in the matrix already begun by Hartwig, Neumann, and Rose and by Neumann and Schneider.
120497198
A maximality theorem concerning extreme points
122751787
Varianten zum Konvergenzsatz von Simons und Anwendungen in der Choquettheorie
120206552
Beschränktheitsaussagen für sublineare und bisublineare Funktionale
123207765
On the Strassen disintegration theorem
121595993
Continuity of sublinear operators on F-spaces
In this note, some of the fundamental theorems concerning the automatic continuity of positive linear functionals and positive linear operators (see [9,14,21]) as well as certain uniform boundedness type theorems (see [5,13,15,19]) will be extended to derive various continuity properties of (even discontinuous) sublinear operators from some metrizable topological vector space to some ordered topological vector space.