PPU Research Repository
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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.2021-04-21T08:22:02ZTotal nonnegativity of the extended Perron complement
http://scholar.ppu.edu/handle/123456789/2228
Total nonnegativity of the extended Perron complement
Adm, Mohammad; Garloff, Jürgen
A real matrix is called totally nonnegative if all of its minors are nonnegative. In this paper the extended Perron complement of a principal submatrix in a matrix A is investigated. In extension of known results it is shown that if A is irreducible and totally nonnegative and the principal submatrix consists of some specified consecutive rows then the extended Perron complement is totally nonnegative. Also inequalities between minors of the extended Perron complement and the Schur complement are presented.
2016-11-01T00:00:00ZInvariance of total nonnegativity of a matrix under entry-wise perturbation and subdirect sum of totally nonnegative matrices
http://scholar.ppu.edu/handle/123456789/2227
Invariance of total nonnegativity of a matrix under entry-wise perturbation and subdirect sum of totally nonnegative matrices
Adm, Mohammad; Garloff, Jürgen
A real matrix is called totally nonnegative if all of its minors are nonnegative. In this paper, the minors are determined from which the maximum allowable entry perturbation of
a totally nonnegative matrix can be found, such that the perturbed matrix remains totally nonnegative. Also, the total nonnegativity of the first and second subdirect sum of two
totally nonnegative matrices is considered.
2017-02-01T00:00:00ZRelaxing the Nonsingularity Assumption for Intervals of Totally Nonnegative Matrices
http://scholar.ppu.edu/handle/123456789/2226
Relaxing the Nonsingularity Assumption for Intervals of Totally Nonnegative Matrices
Adm, Mohammad; Almuhtaseb, Khawla; Abedel Ghani, Ayed; Garloff, Jürgen
Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and matrix intervals with respect to the checkerboard partial order are considered. It is proven that if the two bound matrices of such a matrix interval are totally nonnegative and satisfy certain conditions then all matrices from this interval are totally nonnegative and satisfy these conditions, too, hereby relaxing the nonsingularity condition in a former paper [M. Adm, J. Garloff, Intervals of totally nonnegative matrices, Linear Algebra Appl. 439 (2013), pp.3796-3806].
2020-03-27T00:00:00ZCharacterization, perturbation, and interval property of certain sign regular matrices
http://scholar.ppu.edu/handle/123456789/2225
Characterization, perturbation, and interval property of certain sign regular matrices
Adm, Mohammad; Garloff, Jürgen
The class of square matrices of order n having a negative determinant and all their minors up to order n-1 nonnegative is considered. A characterization of these matrices is presented which provides an easy test based on the Cauchon algorithm for their recognition. Furthermore, the maximum allowable perturbation of the entry in position (2, 2) such that the perturbed matrix remains in this class is given. Finally, it is shown that all matrices lying between two matrices of this class with respect to the checkerboard ordering are contained in this class, too.
2021-03-01T00:00:00Z