Calculation of the concentrations of the components of a mixture based on its spectrum using pseudoinversion

In‐tube collision‐induced dissociation for selected ion flow‐drift tube mass spectrometry, SIFDT‐MS: a case study of NO+ reactions with isomeric monoterpenes

“…The mathematical approach for calculation of the concentrations of components of a mixture from their overlapping spectrum using pseudoinverse matrix [33] can be used on data from any spectrometric technique including SIFDT-MS, SIFT-MS and PTR-MS. This approach is based on the assumption that the concentration of a compound in the analysed mixture of molecules influences the intensity of the product ion peaks on the mass spectra linearly in direct proportion to its fraction in the mixture.…”

“…where P + is the pseudoinverse matrix of the matrix P. [33] The procedure of the matrix pseudoinversion is necessary here because P is not a square matrix and thus an exact inverse matrix does not exist. When P has linearly independent rows, as in our case (note that this means that necessarily the number of ions must be greater than the number of compounds), the pseudoinverse matrix can be calculated as:…”

Ultraviolet and light absorption spectrometry

“…The simultaneous analysis of pheophytin A and pheophytin B in rapeseed oil employing the pseudoinversion method (201) is just one of many papers in this area dealing with organic compounds. Multiwavelength analysis of food coloring mixtures of tartrazine, sunset yellow, amaranth, indigo, and brilliant blue in beverages has been reported (202).…”