000070708 001__ 70708 000070708 005__ 20200221144242.0 000070708 0247_ $$2doi$$a10.13001/1081-3810.3033 000070708 0248_ $$2sideral$$a106052 000070708 037__ $$aART-2016-106052 000070708 041__ $$aeng 000070708 100__ $$aJohnson, C.R. 000070708 245__ $$aOptimal Gersgorin-style estimation of the largest singular value. II 000070708 260__ $$c2016 000070708 5060_ $$aAccess copy available to the general public$$fUnrestricted 000070708 5203_ $$aIn estimating the largest singular value in the class of matrices equiradial with a given $n$-by-$n$ complex matrix $A$, it was proved that it is attained at one of $n(n-1)$ sparse nonnegative matrices (see C.R.~Johnson, J.M.~Pe{\~n}a and T.~Szulc, Optimal Gersgorin-style estimation of the largest singular value; {\em Electronic Journal of Linear Algebra Algebra Appl.}, 25:48--59, 2011). Next, some circumstances were identified under which the set of possible optimizers of the largest singular value can be further narrowed (see C.R.~Johnson, T.~Szulc and D.~Wojtera-Tyrakowska, Optimal Gersgorin-style estimation of the largest singular value, {\it Electronic Journal of Linear Algebra Algebra Appl.}, 25:48--59, 2011). Here the cardinality of the mentioned set for $n$-by-$n$ matrices is further reduced. It is shown that the largest singular value, in the class of matrices equiradial with a given $n$-by-$n$ complex matrix, is attained at one of $n(n-1)/2$ sparse nonnegative matrices. Finally, an inequality between the spectral radius of a $3$-by-$3$ nonnegative matrix $X$ and the spectral radius of a modification of $X$ is also proposed. 000070708 536__ $$9info:eu-repo/grantAgreement/ES/DGA/FSE$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2015-65433-P 000070708 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000070708 590__ $$a0.475$$b2016 000070708 591__ $$aMATHEMATICS$$b222 / 310 = 0.716$$c2016$$dQ3$$eT3 000070708 592__ $$a0.604$$b2016 000070708 593__ $$aAlgebra and Number Theory$$c2016$$dQ3 000070708 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000070708 700__ $$0(orcid)0000-0002-1340-0666$$aPeña, J.M.$$uUniversidad de Zaragoza 000070708 700__ $$aSzulc, T. 000070708 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000070708 773__ $$g31 (2016), 679-685$$pElectronic Journal of Linear Algebra$$tElectronic Journal of Linear Algebra$$x1537-9582 000070708 8564_ $$s116327$$uhttps://zaguan.unizar.es/record/70708/files/texto_completo.pdf$$yVersión publicada 000070708 8564_ $$s55364$$uhttps://zaguan.unizar.es/record/70708/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000070708 909CO $$ooai:zaguan.unizar.es:70708$$particulos$$pdriver 000070708 951__ $$a2020-02-21-13:21:58 000070708 980__ $$aARTICLE