Abstract
The nonprincipal subdeterminants of a normal matrix satisfy certain quadratic identities. In this paper, these identities are used to obtain upper bounds on such subdeterminants in terms of elementary symmetric functions of the moduli of the eigenvalues. The same analysis yields lower bounds on the spread of a normal matrix and on the Hilbert norm of an arbitrary matrix.
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References
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© 1980 Springer Basel AG
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Marcus, M., Filippenko, I. (1980). Inequalities Connecting Eigenvalues and Nonprincipal Subdeterminants. In: Beckenbach, E.F. (eds) General Inequalities 2. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 47. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6324-7_9
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DOI: https://doi.org/10.1007/978-3-0348-6324-7_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1056-1
Online ISBN: 978-3-0348-6324-7
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