# Mohammad AdmPalestine Polytechnic University · Department of Applied Mathematics

Mohammad Adm

Dr. rer. nat

## About

24

Publications

1,773

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

114

Citations

Citations since 2016

Introduction

Additional affiliations

September 2018 - present

February 2017 - January 2018

February 2017 - July 2018

Education

October 2012 - January 2016

September 2009 - June 2011

January 2005 - June 2008

## Publications

Publications (24)

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...

A matrix is called weakly Hadamard if its entries are from {0,−1,1} and its non-consecutive columns (with some ordering) are orthogonal. Unlike Hadamard matrices, there is a weakly Hadamard matrix of order n for every n≥1. In this work, graphs for which their Laplacian matrices can be diagonalized by a weakly Hadamard matrix are studied. A number o...

In this article, the collection of classes of matrices presented in [J. Garloff, M. Adm, ad J. Titi, A survey of classes of matrices possessing the interval property and related properties, Reliab. Comput. 22:1-14, 2016] is continued. That is, given an interval of matrices with respect to a certain partial order, it is desired to know whether a spe...

We correct an error in the original Lemma 3.4 in our paper “Achievable Multiplicity partitions in the IEVP of a graph”’ [Spec. Matrices 2019; 7:276-290.]. We have re-written Section 3 accordingly.

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 nonnegati...

Associated to a graph G is a set S(G) of all real-valued symmetric matrices whose off-diagonal entries are nonzero precisely when the corresponding vertices of the graph are adjacent, and the diagonal entries are
free to be chosen. If G has n vertices, then the multiplicities of the eigenvalues of any matrix in S(G) partition n; this is called a mu...

Associated to a graph $G$ is a set $\mathcal{S}(G)$ of all real-valued symmetric matrices whose off-diagonal entries are non-zero precisely when the corresponding vertices of the graph are adjacent, and the diagonal entries are free to be chosen. If $G$ has $n$ vertices, then the multiplicities of the eigenvalues of any matrix in $\mathcal{S}(G)$ p...

Given a graph G we are interested in studying the symmetric matrices associated to G with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and co...

For a class of matrices connected with Cauchon diagrams, Cauchon matrices, and the Cauchon algorithm, a method for determining the rank, and for checking a set of consecutive row (or column) vectors for linear independence is presented. Cauchon diagrams are also linked to the elementary bidiagonal factorization of a matrix and to certain types of r...

In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the \emph{closed} left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detai...

We investigate strongly regular graphs for which Hoffman's ratio bound and Cvetcovi\'{c}'s inertia bound are equal. This means that $ve^- = m^-(e^- - k)$, where $v$ is the number of vertices, $k$ is the regularity, $e^-$ is the smallest eigenvalue, and $m^-$ is the multiplicity of $e^-$. We show that Delsarte cocliques do not exist for all Taylor's...

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 o...

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...

We consider classes of (Formula presented.)-by-(Formula presented.) sign regular matrices, i.e. of matrices with the property that all their minors of fixed order (Formula presented.) have one specified sign or are allowed also to vanish, (Formula presented.). If the sign is nonpositive for all (Formula presented.), such a matrix is called totally...

This paper considers intervals of real matrices with respect to partial orders and the problem to infer from some exposed matrices lying on the boundary of such an interval that all real matrices taken from the interval possess a certain property. In many cases such a property requires that the chosen matrices have an identically signed inverse. We...

In this paper totally nonnegative (positive) matrices are considered which are matrices having all their minors nonnegative (positive); the almost totally positive matrices form a class between the totally nonnegative matrices and the totally positive ones. An efficient determinantal test based on the Cauchon algorithm for checking a given matrix f...

A totally positive matrix is a matrix having all its minors positive. The largest amount by which the single entries of such a matrix can be perturbed without losing the property of total positivity is given. Also some completion problems for totally positive matrices are investigated.

Totally nonnegative matrices, i.e., matrices having all minors nonnegative, are considered. A condensed form of the Cauchon algorithm which has been proposed for finding a param-eterization of the set of these matrices with a fixed pattern of vanishing minors is derived. The close connection of this variant to Neville elimination and bidiagonalizat...

Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and matrix intervals with respect to the checkerboard ordering are considered. It is proven that if the two bound matrices of such a matrix interval are nonsingular and totally nonnegative (and in addition all their zero minors are identical) then all matrices from th...

Tridiagonal matrices are considered which are totally nonnegative, i. e., all their minors are nonnegative. The largest amount is given by which the single entries of such a matrix
can be perturbed without losing the property of total nonnegativity.

We apply several matrix inequalities to the derivative companion matrices of complex polynomials to establish new bounds and majorization relations for the critical points of these polynomials in terms of their zeros.