The data. We have observations of A mp ∈ R, the value of property p in material m, for (m, p) ∈ Ω ⊂ {1, 2, ..., M}×{1, 2, ..., P }, which defines Ω as the set of ordered pairs describing the entries in A that are observed. That is, the material-property matrix A ∈ R M×P , whose entry (m, p) is A mp , is not complete; some entries are missing (|Ω| < MP ).