Note on best possible bounds for determinants of matrices close to the identity matrix

We give upper and lower bounds on the determinant of a small perturbation of the identity matrix. The lower bounds are best possible, and in most cases they are stronger than well-known bounds due to Ostrowski and other authors. The upper bounds are best possible if a skew-Hadamard matrix of the same order exists. (C) 2014 Elsevier Inc. All rights reserved.