Bounds for characteristic roots of matrices

摘要: which has the roots 0, -3, 5. The root 0 is contained in all three circles. It can however be shown that an analogue of situation for n = 2 holds if further conditions are imposed on elements aik. Theorem 1. dominant a matrix positive canno t common point circles Oi unless it boundary at least two Proof. known [2] A such real and corresponding characteristic vector XI, ... , Xn chosen way its components posi tive. Consider then equation