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Titolo: Decomposition theorems for conditional signsolvability and signsolvability of general systems
Autore: Cokus, S; Klee, V;
 Indirizzi:
 Univ Washington, Dept Math, Seattle, WA 98195 USA Univ Washington SeattleWA USA 98195 on, Dept Math, Seattle, WA 98195 USA
 Titolo Testata:
 SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
fascicolo: 3,
volume: 21,
anno: 2000,
pagine: 978  988
 SICI:
 08954798(20000309)21:3<978:DTFCSA>2.0.ZU;21
 Fonte:
 ISI
 Lingua:
 ENG
 Keywords:
 signsolvable; conditionally signsolvable; decomposition; sign cone; relatively open; Lmatrix; Smatrix; CSmatrix; Lsystem; Ssystem; CSsystem;
 Tipo documento:
 Article
 Natura:
 Periodico
 Settore Disciplinare:
 Physical, Chemical & Earth Sciences
 Citazioni:
 9
 Recensione:
 Indirizzi per estratti:
 Indirizzo: Cokus, S Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA Univ Washington Box 354350 Seattle WA USA 98195 tle, WA 98195 USA



 Citazione:
 S. Cokus e V. Klee, "Decomposition theorems for conditional signsolvability and signsolvability of general systems", SIAM J MATR, 21(3), 2000, pp. 978988
Abstract
For each m x n real matrix A, let Null(A) be the right nullspace of A and let Q (A) be the set of m x n real matrices with the same sign pattern as A. If it is true for all (A) over tilde is an element of Q (A) that (i) Null((A) over tilde) = {0}, then A is an L  matrix, and if it is true for all (A) over tilde is an element of Q (A) that (ii) Null((A) over tilde) is a line penetrating the open positive orthant of Rn, then A is an Smatrix. When (i) or (ii) holds for each (A) over tilde is an element of Q (A) and (ii) applies to at least one, then A is a CSmatrix. It is known that the study of signsolvability of linear systems may be decomposed into the study ofL and Smatrices, while the study of conditional signsolvability may be decomposed into that of L and CSmatrices. When signsolvability and conditional signsolvability are regarded as properties of systems of sign conesin Rm associated with the relevant matrices columns, they have natural generalizations to systems of arbitrary subsets of Rm. This paper contains extended decomposition results for arbitrary systems in the case of signsolvability, and in the case of conditional signsolvability, for arbitrary systems of subsets in which each subset is relatively open in its linear span.
ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 28/01/21 alle ore 06:22:11