Full spark frames and totally positive matrices

In this paper we establish a connection between full spark frames and totally nonsingular matrices. Then we provide a method for constructing infinite totally positive matrices which make up a subclass of the class of totally nonsingular matrices. Using this method we then construct a family of infinite totally positive matrices parameterized by non-negative numbers which contains, as the simplest case, the infinite Pascal matrix. The paper ends with some examples and comments on full spark frames.     

A Sufficient condition for strict total positivity of a matrix

We establish a sufficient condition for strict total positivity of a matrix In particular, we show that if the (positive) elements of a square matrix grow sufficiently fast as their distance from the diagonal of the matrix increases, then the matrix is strictly totally positive.