Polynomials and numerical ranges

Author:
Chi-Kwong Li

Journal:
Proc. Amer. Math. Soc. **104** (1988), 369-373

MSC:
Primary 15A60; Secondary 15A69, 26C10

DOI:
https://doi.org/10.1090/S0002-9939-1988-0962800-3

MathSciNet review:
962800

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an complex matrix. For we study the inclusion relation for the following polynomial sets related to the matrix .

(a) The classical numerical range of the th compound of the matrix .

(b) The th decomposable numerical range of the matrix .

(c) The convex hull of the set of all monic polynomials of degree that divide the characteristic polynomial of . Moreover, we give an example showing that the set described in (a) is not convex in general. This settles a question raised by C. Johnson.

**[1]**Y. H. Au-Yeung and N. K. Tsing,*An extension of the Hausdorff-Toeplitz theorem on the numerical range*, Proc. Amer. Math. Soc.**89**(1983), 215-218. MR**712625 (85f:15021)****[2]**K. Fan and G. Pall,*Imbedding conditions for hermitian and normal matrices*, Canad. J. Math.**9**(1957), 298-304. MR**0085216 (19:6e)****[3]**C. R. Johnson,*Interlacing polynomial*, Proc. Amer. Math. Soc.**100**(1987), 401-404. MR**891133 (88h:15049)****[4]**M. Marcus,*Finite dimensional multilinear algebra*. I and II, Marcel Dekker, 1973 and 1975.**[5]**M. Marcus and I. Filippenko,*Linear operators preserving the decomposable numerical range*, Linear and Multilinear Algebra**7**(1979), 27-36. MR**523645 (80d:15028)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
15A60,
15A69,
26C10

Retrieve articles in all journals with MSC: 15A60, 15A69, 26C10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0962800-3

Keywords:
Numerical range,
decomposable numerical range,
characteristic polynomial

Article copyright:
© Copyright 1988
American Mathematical Society