Figure : Elucidating the unresponsive and ranked responsive directions of a (toy) sensor array through the singular value decomposition (SVD) of the Jacobian matrix J of its adsorption function a(x). (a) A gravimetric, two-MOF sensor array immersed in a four-component gas mixture at constant temperature and pressure but varying composition. The gas composition x ∈ R 3 , while the sensor response m ∈ R 2 . (b) The adsorption function a(x) is a map a : x → m from 3D gas composition space (left) to 2D sensor response space (right). The operating gas composition x op and associated response m op are shown as black points. Under the linear approximation of a(x) valid locally around x op : The image of the sphere of small radius (blue, left) maps to the solid ellipse (blue, right) with semi-major and semi-minor axes given by σ 1 u 1 and σ 2 u 2 , respectively. Gas composition changes v 1 , v 2 , v 3 form an orthogonal basis of composition space and are mapped to response changes σ 1 u 1 , σ 2 u 2 , 0, respectively. v 3 describes the unresponsive direction, since small changes in composition in this direction do not alter the response. Small composition changes in the direction of v 1 elicit the largest-magnitude response. (c) The singular value decomposition J = UΣV gives the vectors described in (b). , N 2 (298 K) , CO 2 (298 K) , and C 2 H 6 (296 K) , and adsorption isotherm data (•, , +, and x, respectively) in HKUST-1 and Co-MOF-74. Lines show the pure-component adsorption models fit to the data.