Copyright © 2010 Hou-Biao Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some new upper and lower bounds on determinants are presented for diagonally dominant matrices and general H-matrices by using different methods. These bounds are some improvements of results given by Ostrowski (1952) and (1937), Price (1951), Wang and Zhang (2002), Huang and Liu (2005), and so forth. In addition, these bounds are also used to localize some numerical characters (e.g., the minimum eigenvalues, singular values and condition numbers) of certain matrices.