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Some Geometrical Properties of the Decomposable Numerical Range
Cheng,Che Man1; Li,Chi Kwong2
Source PublicationLinear and Multilinear Algebra
AbstractFor 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.
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Scopus ID2-s2.0-0346623913
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Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.Faculty of Science and Technology,University of Macau,Macau,China
2.Department of Mathematics,The College of William and Mary,Williamsburg, VA 23187,United States
First Author AffilicationFaculty of Science and Technology
Recommended Citation
GB/T 7714
Cheng,Che Man,Li,Chi Kwong. Some Geometrical Properties of the Decomposable Numerical Range[J]. Linear and Multilinear Algebra,1994,37(1-3):207-212.
APA Cheng,Che Man,&Li,Chi Kwong.(1994).Some Geometrical Properties of the Decomposable Numerical Range.Linear and Multilinear Algebra,37(1-3),207-212.
MLA Cheng,Che Man,et al."Some Geometrical Properties of the Decomposable Numerical Range".Linear and Multilinear Algebra 37.1-3(1994):207-212.
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