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

Matrix inequalities and the additive inverse eigenvalue problem

  • G. N. de Oliveira


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.


Real Number Computational Mathematic Eigenvalue Problem Present Note Inverse Eigenvalue Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Matrix-Ungleichungen und das additive inverse Eigenwertproblem


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Hadeler, K. P.: Ein inverses Eigenwertproblem. Linear Algebra and its Applications,1, 83–101 (1968).Google Scholar
  2. [2]
    Laborde, Françoise: Sur un problème inverse d'un problème de valeurs propres. C. R. Acad. Sc. Paris268, 153–156 (1969).Google Scholar
  3. [3]
    Mirsky, L.: Inequalities for normal andHermitian matrices. Duke J. Math.24, 591–599 (1957).Google Scholar
  4. [4]
    de Oliveira, G. N.: Note on an inverse characteristic value problem. Num. Math.15, 345 to 347 (1970).Google Scholar
  5. [5]
    de Oliveira, G. N.: Note on the additive inverse eigenvalue problem. Rev. Fac. C. Lisboa13, 21–26 (1970).Google Scholar
  6. [6]
    De Oliveira, G. N.: On the multiplicative inverse eigenvalue problem. To appear in Canadian Math. Bull.Google Scholar
  7. [7]
    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

Personalised recommendations