On Some Properties for the Sequence of Brualdi-Li Matrices - Xiaogen Chen (Journal of Applied Mathematics)
Let B2n denote the Brualdi-Li matrix, and let ρ2n=ρ(B2n) denote the Perron value of the Brualdi-Li matrix of order 2n. We prove that 2n(n-1/2-ρ2n) is monotonically decreasing for all n and ρ2n<n-1/2-(e2-1)/4(e2+1)n, where e=2.718281828459045….