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Some Results on Matrices with Prescribed Diagonal Elements and Singular Values

Published online by Cambridge University Press:  20 November 2018

Fuk-Yum Sing
Fuk-Yum Sing*
Affiliation:
University of Hong Kong, Hong Kong
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Let A be an n × n complex matrix. The singular values of A are the non-negative square-roots of the eigenvalues of A*A. G. N. De Oliviera [4] gave a necessary condition for the existence of a matrix A with a1..., an as diagonal elements and α1,..., αn as singular values. We shall give another necessary condition which implies the above author’s condition and we show that this is also a sufficient condition for the case n =2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 1 , 01 March 1976 , pp. 89 - 92
Copyright
Copyright © Canadian Mathematical Society 1976

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. Horn, A., Doubly stochastic matrices and diagonal of a rotation matrix, Amer. J. of Math. 76(1954)620–630.Google Scholar
3. Mirsky, L., On a convex set of matrices, Arch. Math. Vol. 10 (1959), 88–92.Google Scholar
4. De Oliviera, G. N. , Matrices with prescribed principal elements and singular values, Canad. Math. Bull. 14 (2), 1971, 247–249.Google Scholar