The total positivity interval Original Research Article

If Aset membership, variantMn is totally positive (TP), we determine the maximum open interval image around the origin such that, if image, then A−μI is TP. If A is TP, image and A−μI=LU, then B defined by B−μI=UL is TP, and has the same total positivity interval image. If A is merely nonsingular and totally nonnegative (TN), or oscillatory, there need be no such interval in which A−μI is TN.