Eigenvalue bounds for some classes of  P ‐matrices | Zendy

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Eigenvalue bounds for some classes of P ‐matrices

Author(s) -

Peña J. M.

Publication year - 2009

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.660

Subject(s) - mathematics , diagonally dominant matrix , eigenvalues and eigenvectors , diagonal , invertible matrix , combinatorics , sign (mathematics) , matrix (chemical analysis) , upper and lower bounds , diagonal matrix , m matrix , pure mathematics , mathematical analysis , geometry , physics , materials science , composite material , quantum mechanics

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.

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