title: Complex numbers in chemometrics: examples from multivariate impedance measurements on lipid monolayers.
abstract: Electrical impedance gives multivariate complex number data as results. Two examples of multivariate electrical impedance data measured on lipid monolayers in different solutions give rise to matrices (16x50 and 38x50) of complex numbers. Multivariate data analysis by principal component analysis (PCA) or singular value decomposition (SVD) can be used for complex data and the necessary equations are given. The scores and loadings obtained are vectors of complex numbers. It is shown that the complex number PCA and SVD are better at concentrating information in a few components than the naïve juxtaposition method and that Argand diagrams can replace score and loading plots. Different concentrations of Magainin and Gramicidin A give different responses and also the role of the electrolyte medium can be studied. An interaction of Gramicidin A in the solution with the monolayer over time can be observed.
authors.affiliation: Unit of Biomass Technology and Chemistry, Swedish University of Agricultural Sciences, Box 4097, SE 90403 Umeå, Sweden. paul.geladi@btk.slu.se
authors.forename: Paul
authors.initials: P
authors.lastname: Geladi
authors.forename: Andrew
authors.initials: A
authors.lastname: Nelson
authors.forename: Britta
authors.initials: B
authors.lastname: Lindholm-Sethson
mesh_terms: D017097:Electric Impedance; D004563:Electrochemistry / Q000379:methods; D008055:Lipids / Q000032:analysis / Q000592:standards; D015999:Multivariate Analysis; D053835:Unilamellar Liposomes / Q000032:analysis* / Q000592:standards*
chemical_list: D008055:Lipids; D053835:Unilamellar Liposomes