Equality of higher-rank numerical ranges of matrices

Chi Tung Chang, Hwa Long Gau, Kuo Zhong Wang

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)

摘要

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 ≤k1k2 ≤ 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).

原文???core.languages.en_GB???
頁(從 - 到)626-638
頁數13
期刊Linear and Multilinear Algebra
62
發行號5
DOIs
出版狀態已出版 - 5月 2014

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