Equality of higher-rank numerical ranges of matrices

Chi Tung Chang, Hwa Long Gau, Kuo Zhong Wang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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).

Original languageEnglish
Pages (from-to)626-638
Number of pages13
JournalLinear and Multilinear Algebra
Issue number5
StatePublished - May 2014


  • compression
  • higher-rank numerical range
  • numerical range
  • principal submatrix


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