Chapter 29
Totally Positive and Totally Nonnegative Matrices
Shaun M. Fallat
University of Regina
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 Ax for fixed A [Sch30]. Since then this class (and the more general 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 nonnegative matrices) that, over the years, many convenient ...
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