Abstract :
A real matrix Aset membership, variantMn is TP (totally positive) if all its minors are nonnegative; NTP, if it is non-singular and TP; STP, if it is strictly TP; O (oscillatory) if it is TP and a power Am is STP. We consider the Toda flow of a symmetric matrix A(t), and show that if A(0) is one of TP, NTP, STP or O, then A(t) is TP, NTP, STP or O, respectively.
