Stability of the orthogonality preserving property in finite-dimensional inner product spaces

We establish a stability property for inner product preserving (not necessarily linear) mappings. Then, as a consequence, we show that a linear mapping, defined on a finite-dimensional inner product space, which approximately preserves orthogonality can be approximated by a linear, orthogonality preserving one. (c) 2005 Elsevier Inc. All rights reserved.