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A remark on the generalized numerical range of a normal matrix

Published online by Cambridge University Press:  18 May 2009

Yik-Hoi Au-Yeung  and
Fuk-Yum Sing
Yik-Hoi Au-Yeung
Affiliation:
Department of Mathematics, University of Hong Kong
Fuk-Yum Sing
Affiliation:
Department of Mathematics, University of Hong Kong
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Let A be an n × n complex normal matrix and let (A) = {diag UAU*: U is unitary) where U* is the conjugate transpose of U. It is known that (A) may not be convex [1, 3] and it is convex when A is Hermitian [1, 2]. In this note we show that (A) is convex if and only if the eigenvalues of A are collinear (i.e. there exist complex numbers α ( ≠ 0) and β such that αA + βi is Hermitian).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 2 , July 1977 , pp. 179 - 180
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

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