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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 a 1..., a n 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.

Information

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