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Matrices and spectra satisfying the Newton inequalities

✍ Scribed by C.R. Johnson; C. Marijuán; M. Pisonero

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
190 KB
Volume
430
Category
Article
ISSN
0024-3795

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✦ Synopsis

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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Generalized Clarkson's Inequalities and
Generalized Clarkson's Inequalities and the Norms of the Littlewood Matrices
✍ Mikio Kato 📂 Article 📅 1983 🏛 John Wiley and Sons 🌐 English ⚖ 245 KB

By using the LITTLEWOOD matrices B g n we generalize CLAEKSON'S inequelitiee, or equivalently, we determine the norms IIAzn : Z,2"(Lp) + Zr(Lp)ll completely. The result is compared with the norms IIAp : 1,2" -+ Zrl l , which are calculated implicitly in PIETSOE [el.