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Matrices and spectra satisfying the Newton inequalities

Pisonero, M.
; 
Johnson, C. R.
; 
Pisonero, M.
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. (C) 2009 Elsevier Inc. All rights reserved.
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2009-01-01
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Mathematics
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Matrices_and_spectra.pdf
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Mathematics
DOI
10.1016/j.laa.2009.01.019
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https://scholarworks.wm.edu/handle/internal/448
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