#### Document Type

Article

#### Department/Program

Mathematics

#### Pub Date

10-2016

#### Place of Publication

ELECTRONIC JOURNAL OF LINEAR ALGEBRA

#### Volume

31

#### Abstract

In 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. Penna and T. Szulc, Optimal Gersgorin-style estimation of the largest singular value; 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, 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.

#### Recommended Citation

Johnson, Ch. R.; Pena, J. M.; and Szulc, T., Optimal Gersgorin-Style Estimation Of The Largest Singular Value, Ii (2016).

10.13001/1081-3810.3033

#### DOI

10.13001/1081-3810.3033