Computing

, Volume 9, Issue 2, pp 95–100 | Cite as

Matrix inequalities and the additive inverse eigenvalue problem

  • G. N. de Oliveira
Article

Summary

LetA be anHermitiann×n matrix ands1, ...,sn real numbers; under what conditions does there exist a diagonal realn×n matrixM such thatA+M has eigenvaluess1, ...,sn? In the present note we prove a matrix inequality which gives a necessary condition for this problem to have a solution.

Keywords

Real Number Computational Mathematic Eigenvalue Problem Present Note Inverse Eigenvalue Problem 

Matrix-Ungleichungen und das additive inverse Eigenwertproblem

Zusammenfassung

A sei eine Hermitischenn×n Matrix unds1, ...,sn reelle Zahlen; unter welchen Bedingungen gibt es ein rellen×n Matrix,M, so daßA+M Eigenwertes1, ...,sn hat? In dieser Arbeit beweisen wir eine Matrix-Ungleichung, die eine notwendige Bedingung für die Lösung dieses Problems gibt.

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References

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    Laborde, Françoise: Sur un problème inverse d'un problème de valeurs propres. C. R. Acad. Sc. Paris268, 153–156 (1969).Google Scholar
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    Mirsky, L.: Inequalities for normal andHermitian matrices. Duke J. Math.24, 591–599 (1957).Google Scholar
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    de Oliveira, G. N.: Note on an inverse characteristic value problem. Num. Math.15, 345 to 347 (1970).Google Scholar
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    de Oliveira, G. N.: Note on the additive inverse eigenvalue problem. Rev. Fac. C. Lisboa13, 21–26 (1970).Google Scholar
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    De Oliveira, G. N.: On the multiplicative inverse eigenvalue problem. To appear in Canadian Math. Bull.Google Scholar
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    De Oliveira, G. N.: Inverse eigenvalue problems for complex matrices. Computing6, 339–341 (1970).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • G. N. de Oliveira
    • 1
  1. 1.Instituto de MatemáticaUniversidade Federal de PernambucoRecife-PeBrazil

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