A matrix is totally uni-modular if the determinant of any (square) sub-matrix is {+1, 0, -1}. My question is, "Is there a way to transform(linear or non) a general matrix into a totally uni-modular matrix?" or, "Are there only certain matrices that can be transformed in such a way?" This is for an application in Linear (convex) optimization.
Thanks
Edit:
As a linear-based method, I was thinking more of multiplying the starting matrix by a Gaussian matrix (or some other distribution) and then using the sign() function to restrict the values to {-1,1} with small values probably set to 0. I mostly want to see it anyone knows any transformations for restricting values.