ABSTRACT
Total positivity has been a recurring theme in linear algebra and other aspects of mathematics for the past 80 years. Totally positive matrices, in fact, originated from studying small oscillations in mechanical systems [GK60], and from investigating relationships between the number of sign changes of the vectors x and A x for fixed A [Sch30]. Since then this class (and the related class of sign-regular matrices) has arisen in such a wide range of applications (see [GM96] for an incredible compilation of interesting articles dealing with a long list of relevant applications of totally positive matrices) that over the years many convenient points of view for total positivity have been offered and later defended by many prominent mathematicians.
