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Matrices with Prescribed Principal Elements and Singular Values

Published online by Cambridge University Press:  20 November 2018

Graciano N. De Oliveira
Graciano N. De Oliveira*
Affiliation:
Instituto Gulbenkian de Ciencia, C.C.C., Oeiras, Portugal
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We shall be concerned with the following problem. Let a11, …, ann be complex numbers and λ1, …, λn nonnegative real numbers. Under what conditions does there exist an n × n complex matrix A with a11, …, ann as principal elements and λ1, …, λn as singular values? This problem has been suggested in [3] but, to our knowledge, has not yet been solved.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 247 - 249
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Horn, A., On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954), 4-7.Google Scholar
2. Mirsky, L., Matrices with prescribed characteristic roots and diagonal elements, J. London Math. Soc. 33 (1958), 14-21.Google Scholar
3. Mirsky, L., Inequalities and existence theorems in the theory of matrices, J. Math. Anal. Appl. 9(1964), 99-118.Google Scholar
4. Thompson, R. C., Principal submatrices IX: Interlacing inequalities for singular values of submatrices, Linear Algebra and its Applications (to appear).Google Scholar