Matrices and spectra satisfying the Newton inequalities |
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Authors: | CR Johnson C Marijun M Pisonero |
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Institution: | aDepartment of Mathematics, College of William and Mary, Williamsburg, VA 23187, USA;bDpto. Matemática Aplicada, E.T.S.I. Informática, Campus Miguel Delibes s/n, 47011 Valladolid, Spain;cDpto. Matemática Aplicada, E.T.S. de Arquitectura, Avenida de Salamanca s/n, 47014 Valladolid, Spain |
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Abstract: | An n-by-n real matrix is called a Newton matrix (and its eigenvalues a Newton spectrum) if the normalized coefficients of its characteristic polynomial satisfy the Newton inequalities.A number of basic observations are made about Newton matrices, including closure under inversion, and then it is shown that a Newton matrix with nonnegative coefficients remains Newton under right translations. Those matrices that become (and stay) Newton under translation are characterized. In particular, Newton spectra in low dimensions are characterized. |
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Keywords: | Determinantal inequalities Newton inequalities Newton matrix Translation |
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