Some improvements of a Ky Fan theorem are presented for matrix eigenvalue inclusion problems. Subsequently, we investigate the relationships between K0(A), the union of Ky Fan theorem sets, S(A), the union of the Theorem 2.1 sets, and S1(A), the union of the Theorem 2.2 sets, for eigenvalue inclusions of an n × n complex matrix A. If σ(A) denotes the spectrum of A, we show thatσ(A)⊆S(A)⊆K1(A)⊆K0(A) is valid for any weakly irreducible n × n complex matrix A with n < 2. © 2005 Elsevier Ltd. All rights reserved.
Li, H. B., & Huang, T. Z. (2005). An improvement of Ky Fan theorem for matrix eigenvalues. Computers and Mathematics with Applications, 49(5–6), 789–803. https://doi.org/10.1016/j.camwa.2004.07.019