A REMARK ON BOUNDEDNESS OF THE NUMERICAL RANGE

CHI FAI CHAN

doi:10.5556/j.tkjm.22.1991.4611

A REMARK ON BOUNDEDNESS OF THE NUMERICAL RANGE

Authors

CHI FAI CHAN Department of Mathematics, University of Hong Kong, Hong Kong.

DOI:

https://doi.org/10.5556/j.tkjm.22.1991.4611

Keywords:

boundedness of the numerical range, Hermitian matrix, minimum (maximum) eigenvalue, counter-example, complex matrices

Abstract

It is shown that Chien's result on the smallest rectangle wjth sjdes parallel to the axes containing the nwnerical range of a real matrix follows from a simple observation on complex matrices. A counter-example to Chien's conjecture is also given.

References

M. T. Chien, "Boundedness of the numerical range", Linear Algebra Appl.·134, 25-30, 1990.

F. R. Gantmacher, The. Theory of Matrices, Vol. I, Chelsea Publishing Company, New York, 1959.

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Published

1991-09-01

How to Cite

CHAN, C. F. (1991). A REMARK ON BOUNDEDNESS OF THE NUMERICAL RANGE. Tamkang Journal of Mathematics, 22(3), 271–273. https://doi.org/10.5556/j.tkjm.22.1991.4611