Eigenvalue bounds for some classes of P‐matrices
Juan Manuel Peña · Numerical Linear Algebra with Applications · 2009
Abstract Eigenvalue bounds are provided. It is proved that the minimal eigenvalue of a Z‐matrix strictly diagonally dominant with positive diagonals lies between the minimal and the maximal row sums. A similar upper bound does not hold for the minimal eigenvalue of a matrix strictly diagonally dominant with positive diagonals but with off‐diagonal entries with arbitrary sign. Other new bounds for nonsingular M‐matrices and totally nonnegative matrices are obtained. Copyright © 2009 John Wiley & Sons, Ltd.