Minimal-volume projections of cubes and totally unimodular matrices Original Research Article

Among all linear projections onto a given linear subspace L in Rn we select those that minimize the volume of the image of the cube {x:xiless-than-or-equals, slant1}. The paper is devoted to a description of the shape of such images of the cube. The shape is characterized in terms of zonotopes spanned by scalar multiples of rows of totally unimodular matrices.