The left singular vector u i ∈ M is column i of U and lies in sensor response space. The right singular vector v i ∈ X is column i of V and lies in gas composition space. The M left (G right) singular vectors form an orthonormal basis for sensor response (gas composition) space. Provided the MOFs are distinct, it is extremely likely that J is full-rank (rank M ) §, so we assume σ M > 0 in this work.