Kirkland, Steve A note on the sequence of Brualdi-Li matrices. (English) Zbl 0865.15014 Linear Algebra Appl. 248, 233-240 (1996). Author’s abstract: We consider the sequence \(2n(n- {1\over 2} -\rho_{2n})\), where \(\rho_{2n}\) is the Perron value of the Brualdi-Lie matrix of order \(2n\) [cf. R. A. Brualdi and Q. Li, Problem 31, Discrete Math. 43, 329-330 (1983)]. We prove that the sequence converges, find its limit, and show that asymptotically, the sequence is monotonically decreasing. In particular, this addresses some problems raised by S. Friedland and M. Katz [Linear Algebra Appl. 208-209, 455-469 (1994; Zbl 0807.15007)]. Reviewer: N.J.Pullman (Kingston/Ontario) Cited in 8 Documents MSC: 15B36 Matrices of integers 15A18 Eigenvalues, singular values, and eigenvectors Keywords:sequence of Brualdi-Lie matrices; convergence; Perron value Citations:Zbl 0807.15007 PDFBibTeX XMLCite \textit{S. Kirkland}, Linear Algebra Appl. 248, 233--240 (1996; Zbl 0865.15014) Full Text: DOI References: [1] Brauer, A.; Gentry, I., On the characteristic roots of tournament matrices, Bull. Amer. Math. Soc., 74, 1133-1135 (1968) · Zbl 0167.03002 [2] Brualdi, R. A.; Li, Q., Problem 31, Discrete Math., 43, 329-330 (1983) [3] Friedland, S., Eigenvalues of almost skew-symmetric matrices and tournament matrices, (Brauldi, R. A.; Friedland, S.; Klee, V., Combinatorial and Graph Theoretic Problems in Linear Algebra. Combinatorial and Graph Theoretic Problems in Linear Algebra, IMA Vol. Math. Appl., 50 (1993), Springer-Verlag: Springer-Verlag New York), 189-206 · Zbl 0789.15019 [4] Friedland, S.; Katz, M., On the maximal spectral radius of even tournament matrices and the spectrum of almost skew-symmetric compact operators, Linear Algebra Appl., 208, 455-469 (1994) · Zbl 0807.15007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.