Eigenvalue bounds for some classes of P‐matrices
Copyright policy )Eigenvalue bounds for some classes of P‐matrices
AbstractEigenvalue 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.
- University of Zaragoza Spain
norm for the inverse, Positive matrices and their generalizations; cones of matrices, \(P\)-matrix, \(M\)-matrix, totally nonnegative matrix, \(Z\)-matrix, minimal eigenvalue, diagonal dominance, Inequalities involving eigenvalues and eigenvectors
norm for the inverse, Positive matrices and their generalizations; cones of matrices, \(P\)-matrix, \(M\)-matrix, totally nonnegative matrix, \(Z\)-matrix, minimal eigenvalue, diagonal dominance, Inequalities involving eigenvalues and eigenvectors
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