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Boundary generating curves of the c-numerical range

✍ Scribed by Mao-Ting Chien; Hiroshi Nakazato

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 150 KB
Volume: 294
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(99)00055-5

No coin nor oath required. For personal study only.

✦ Synopsis

Let A be an n Â n matrix and 1 Y 2 Y F F F Y n be a real n-tuple. The c-numerical range of A is the set e f n j1 j x Ã j ex j X fx 1 Y x 2 Y F F F Y x n g is an orthonormal basis of C n g. We obtain parametric representations of the boundary generating curve of the cnumerical range of a matrix. Applying this result, we generalize the result of Anderson to the c-numerical range. Furthermore, we give a description of the boundary generating curve of the c-numerical range of certain types of nilpotent Toeplitz matrices. A sucient condition for the boundary generating curve to be rational is obtained. Finally we explicitly compute the boundary generating curves of the numerical ranges for several concrete matrices and classify the rationality of the curves.

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