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Titolo:
Decomposition theorems for conditional sign-solvability and sign-solvability 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:
0895-4798(20000309)21:3<978:DTFCSA>2.0.ZU;2-1
Fonte:
ISI
Lingua:
ENG
Keywords:
sign-solvable; conditionally sign-solvable; decomposition; sign cone; relatively open; L-matrix; S-matrix; CS-matrix; L-system; S-system; CS-system;
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 sign-solvability and sign-solvability of general systems", SIAM J MATR, 21(3), 2000, pp. 978-988

## 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 R-n, then A is an S-matrix. 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 CS-matrix. It is known that the study of sign-solvability of linear systems may be decomposed into the study ofL- and S-matrices, while the study of conditional sign-solvability may be decomposed into that of L- and CS-matrices. When sign-solvability and conditional sign-solvability are regarded as properties of systems of sign conesin R-m associated with the relevant matrices columns, they have natural generalizations to systems of arbitrary subsets of R-m. This paper contains extended decomposition results for arbitrary systems in the case of sign-solvability, and in the case of conditional sign-solvability, 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