A totally positive matrix is one whose minors are all positive. This is a simple elementary concept but most of the development on the subject is far from elementary. I am having a hard time understanding most papers on the subject because of the complicated language.
I would like to know, in simple terms, what is known about real totally positive matrices. What are necessary and sufficient conditions for a matrix to be totally positive? What is the simplest known algorithm to verify total positivity?
Thanks in advance.