Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-05T15:33:26.759Z Has data issue: false hasContentIssue false
  • English
  • Français

Matrices with prescribed characteristic polynomial and principal blocks

Published online by Cambridge University Press:  20 January 2009

G. N. De Oliveira
G. N. De Oliveira
Affiliation:
Instituto de Matemática, 3000 Coimbra, 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.

Let A be a matrix over a field Φ partitioned as follows

where A11 is n×n and A22 is m×m. The objective of the present paper is to give further results on the problems mentioned in Section 1 of (3). Concretely we shall consider the following question: “we prescribe the characteristic polynomial f(λ) = λn+m−c1λn+m−1 + … of A and the principal blocks A11, A22. Find a necessary and sufficient condition for the existence of A satisfying these prescribed conditions”.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 24 , Issue 3 , October 1981 , pp. 203 - 208
Copyright
Copyright © Edinburgh Mathematical Society 1981

References

REFERENCES

(1)Farahat, H. and Ledermann, W., Matrices with prescribed characteristic polynomial, Proc. Edinburgh Math. Soc. 11 (1959), 143–146.CrossRefGoogle Scholar
(2)Gantmacher, F. R., The Theory of Matrices (Chelsea Publishing Company, New York, 1960).Google Scholar
(3)De Oliveira, G. N., Matrices with prescribed characteristic polynomial and several prescribed submatrices, Linear Mult. Alg. 2 (1975), 357–364.CrossRefGoogle Scholar
(4)de Oliveira, G. N., Marques de SÁ, E. and Dias da Silva, J. A., On the eigenvalues of the matrix A + XBX−1, Linear Mult. Alg. 5 (1977), 119–128.Google Scholar
(5)Dias Da Selva, J. A., Matrices with prescribed entries and characteristic polynomial, Proc. Amer. Math. Soc. 45 (1974), 31–37.CrossRefGoogle Scholar
(6)Thornton, B. S., Inversion of the geophysical inverse problem for n layers with nonuni-queness reduced to n cases, Geophysics 44 (1979), 801–819.Google Scholar
(7)Wimmer, H. K., Existenzsätze in der Theorie der Matrizen und Lineare Kontrolltheorie, Monatsh. Math. 78 (1974), 256–263.CrossRefGoogle Scholar