@article{be6bb5ca9386471897fcc9975ee4cef9,
title = "Equality of higher-rank numerical ranges of matrices",
abstract = "Let Λk (A) denote the rank-k numerical range of an n-by-n complex matrix A. We give a characterization for Λk1 (A) = Λk2 (A), where 1 ≤k1 ≤k2 ≤ n, via the compressions and the principal submatrices of A. As an application, the matrix A satisfying W(A) = Λk (A), where W(A) is the classical numerical range of A and 1 ≤ k ≤ n, is under consideration. We show that if W(A) = Λk (A) for some k > n/3, then A is unitarily similar to B ⊗ B ⊗ ... ⊗ B⊗C, where B is a 2-by-2 matrix, C is a (3n - 6k)-by-(3n - 6k) matrix and W(A) = W(B) = W(C) Λn-2k (C).",
keywords = "compression, higher-rank numerical range, numerical range, principal submatrix",
author = "Chang, {Chi Tung} and Gau, {Hwa Long} and Wang, {Kuo Zhong}",
note = "Funding Information: We appreciate the advice from Professor Pei Yuan Wu. He pointed out that there exists an 6-by-6 unitarily irreducible matrix A such that W(A) = Λ2(A) and therefore, the number n/3 in Theorem 2.9 (c) is best possible. We also thank the referee for his/her comments, which improved both the statement and the proof of Theorem 2.2. The Research was suppported by the National Science Council of the Republic of China under the projects NSC 101-2115-M-035-006, NSC 101-2115-M-008-006 and NSC 101-2115-M-009-001, respectively.",
year = "2014",
month = may,
doi = "10.1080/03081087.2013.811500",
language = "???core.languages.en_GB???",
volume = "62",
pages = "626--638",
journal = "Linear and Multilinear Algebra",
issn = "0308-1087",
number = "5",
}