Computing

, Volume 9, Issue 2, pp 95–100

# 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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