The basis vectors of unit cell U  can be transformed to basis vectors of supercell S  by linear transformation
where  is a transformation matrix. All elements  should be integers with  (with  the transformation preserves volume).  For example, the matrix
transforms a primitive cell to body-centered. Another particular case of the transformation is a diagonal matrix (i.e., ). This called diagonal supercell expansion and can be represented as repeating of the initial cell over crystallographic axes of the initial cell.