  This paper serves as an introduction to banded totally positive matrices,
exploring various characterizations and associated properties. A significant
result within is the demonstration that the collection of such matrices forms a
semigroup, notably including a subset permitting positive bidiagonal
factorization. Moreover, the paper applies this concept to investigate step
line normality concerning the degrees of associated recursion polynomials. It
presents a spectral Favard theorem, ensuring the existence of measures, thereby
guaranteeing that these recursion polynomials represent mixed multiple
orthogonal polynomials that maintain normality on the step line indices.
