abs_vol20_pp241-253. 25KB Jun 04 2011 12:05:48 AM

(1)

ELA

SOME CHARACTERIZATIONS OF TOTALLY NONPOSITIVE

(TOTALLY NEGATIVE) MATRICES

∗

RAFAEL CANT ´O†_{, BEATRIZ RICARTE}†_, _AND _{ANA M. URBANO}†

Abstract. Ann×_mreal matrix_Ais said to be totally nonpositive (totally negative) if every minor is nonpositive (negative). In this paper, we study characterizations of these classes of matrices by minors, by their full rank factorization and by their thinQRfactorization.

Key words. Totally nonpositive and totally negative matrices, Full rank factorization, Thin QR factorization.

AMS subject classifications.65F40, 15A15, 15A23.

∗_{Received by the editors June 3, 2009. Accepted for publication April 19, 2010. Handling Editor:}

Joao Filipe Queiro.

†_{Institut de Matem`}_{atica Multidisciplinar, Universidad Polit´}_{ecnica de Valencia, 46071 Valencia,}

Spain ([email protected], [email protected], [email protected]). Supported by the Spanish DGI grant MTM2007-64477 and by the UPV under its research program.

Electronic Journal of Linear Algebra ISSN 1081-3810 A publication of the International Linear Algebra Society Volume 20, pp. 241-253, April 2010