Improving certain simple eigenvalue bounds
Seppo Hyydö, Jorma Kaarlo Merikoski, Ari Virtanen · Mathematical Proceedings of the Cambridge Philosophical Society · 1986
Throughout this paper we let A = (aij) be a non-zero n × n matrix-we study real matrices only–with row sums R1,…Rn and eigenvalues λ1,…,λn, ordered λ1≥…≥λn if they are real. We denote E = (1,…,1)T and su A = ΣiΣjaij = ETAE. If A is symmetric, a simple property of the Rayleigh quotient is that satisfies and