Hostname: page-component-5c6d5d7d68-txr5j Total loading time: 0 Render date: 2024-08-15T08:59:19.993Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Multiplicative Inverse Eigenvalue Problem

Published online by Cambridge University Press:  12 February 2019

G. N. De Oliveira
G. N. De Oliveira*
Affiliation:
Instituto Gulbenkian De Ciência, C.C.C., Oeiras, Portugal
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By "multiplicative inverse eigenvalue problem" (m.i.e.p., for short) we mean the following. Let A be an n×n matrix and let s1,…, sn be n given numbers. Under what conditions does there exist an n×n diagonal matrix V such that VA has eigenvalues s1,…,sn?

In the "additive inverse eigenvalue problem" (a.i.e.p., for short) we seek the diagonal matrix V so that A + V has eigenvalues s1,…, sn?.

In the present paper we extend to the m.i.e.p. the ideas used in [7] for the a.i.e.p.

By per X we denote the permanent of the square matrix X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 189 - 194
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Brauer, A., Limits for the characteristic roots of a matrix, Duke Math. J. 13 (1946), 387-395.Google Scholar
2. Brenner, J., Relations among the minors of a matrix with dominant principal diagonal, Duke Math. J. 26 (1959), 563-567.Google Scholar
3. Brenner, J. and Brualdi, R., Eigenschaften der Permanentefunktion, Arch. Math. 18 (1967), 585-586.Google Scholar
4. Ky, Fan, On a theorem of Weyl concerning eigenvalues of linear transformations, Proc.Nat. Acad. Sci. U.S.A. 35 (1949), 652-655.Google Scholar
5. Hadeler, K. P., Multiplicative inverse Eigenwertprobleme, Linear Algebra and its Applications 2 (1969), 65-86.Google Scholar
6. Horn, A., Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), 620-630.Google Scholar
7. de Oliveira, G. N., Note on an inverse characteristic value problem, Numer. Math. 15 (1970), 345-347.Google Scholar
8. de Oliveira, G. N., Note on the additive inverse eigenvalue problem, Rev. Fac. Ci. Lisbo. 13 (1970), 21-26.Google Scholar