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Minkowski, H. (1900) Zur Theorie der Einheiten in den algebraischen Zahlkorper. Nachrichten von der Konigl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universitat zu Gottingen Mathematisch-Physikalische Klasse: Fachgruppe II, Nachrichten aus der Physik, Astronomie, Geophysik, Technik, 90-93.

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• TITLE: Inverse Nonnegativity of Tridiagonal M-Matrices under Diagonal Element-Wise Perturbation

  AUTHORS: Mohamed A. Ramadan, Mahmoud M. Abu Murad

  KEYWORDS: Totally Positive Matrix, Totally Nonnegative Matrix, Tridiagonal Matrices, Compound Matrix, Element-Wise Perturbations

  JOURNAL NAME: Advances in Linear Algebra & Matrix Theory, Vol.5 No.2, June 9, 2015

  ABSTRACT: One of the most important properties of M-matrices is element-wise non-negative of its inverse. In this paper, we consider element-wise perturbations of tridiagonal M-matrices and obtain bounds on the perturbations so that the non-negative inverse persists. The largest interval is given by which the diagonal entries of the inverse of tridiagonal M-matrices can be perturbed without losing the property of total nonnegativity. A numerical example is given to illustrate our findings.