- For an matrix , it maps a point in -dimension to one in -dimension.
Original -dimension is suppressed by and mapped by to the objective space.
- If , the mapping by is to the higher dimension. However, it connot cover that dimension all.
- If , the mapping by is to the lower dimension. So, many points map to one point, which means a kind of suppresion.
- Let . For and , if when , then is injective. If there exists such that for all , then is surjective.
- . It means that the objective space is -dimensional, so is at most .
- . It means that the original space is -dimensional, so is at most although it covers the objective space all.
 Hiraoka Kazuyuki, Hori Gen, Programming No Tame No Senkei Daisu, Ohmsha.