| Abstract | The concept of D-stability is relevant for stable square matrices of any order, especially when they appear in ordinary differential systems modelling physical problems. Indeed, D-stability was treated from different points of view in the last fifty years, but the problem of characterization of a D-stable matrix was solved for low order matrices only (i.e. up to order 4). Here a new approach is proposed within the context of numerical linear algebra. A new necessary and sufficient condition for D-stability is proved and, according to that, an algorithm is implemented by computer algebra. Results show that it is easy and efficient to characterize matrices of order grater than 4. |