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Some Geometrical Properties of the Decomposable Numerical Range
Cheng C.-M.1; Li C.-K.2
1994-06-01
Source PublicationLinear and Multilinear Algebra
ISSN1563-5139
Volume37Issue:1-3Pages:207-212
Abstract

For 1 ≤ m ≤ n, the mth decomposable numerical range of an n × n complex matrix A is defined and denoted by W(A) = {det(X*AX) : X is an n × m complex matrix such that X* X = I}. In this note, we determine the conditions on an essentially Hermitian matrix A (i.e., A is normal with collinear eigenvalues) such that W(A) is (i) convex, or (ii) simply connected. For a general A, we obtain a sufficient for W(A) to be starshaped. These answer some questions raised by Bebiano and the second author on the geometrical properties of the decomposable numerical range. © 1994, Taylor & Francis Group, LLC. All rights reserved.

DOIhttps://doi.org/10.1080/03081089408818322
URLView the original
Language英语
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Document TypeJournal article
专题DEPARTMENT OF MATHEMATICS
Affiliation1.Faculty of Science and Technology , University of Macau , Macau
2.Department of Mathematics , The College of William and Mary , Williamsburg, VA, 23187
First Author AffilicationFaculty of Science and Technology
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Cheng C.-M.,Li C.-K.. Some Geometrical Properties of the Decomposable Numerical Range[J]. Linear and Multilinear Algebra,1994,37(1-3):207-212.
APA Cheng C.-M.,&Li C.-K..(1994).Some Geometrical Properties of the Decomposable Numerical Range.Linear and Multilinear Algebra,37(1-3),207-212.
MLA Cheng C.-M.,et al."Some Geometrical Properties of the Decomposable Numerical Range".Linear and Multilinear Algebra 37.1-3(1994):207-212.
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