An extended version of Principal Components Analysis (PCA) of monument stone decay phenomena occurring at “Basilica da Estrela” church, Lisbon, Portugal, is now presented. This one results from previous studies based mainly on a combined application of multivariate statistical analysis and some traditional geochemical tools. The rationale and the general methodological procedures used in PCA will now be presented, as a first step of a stepwise approach to the eigenvector methods of data analysis. With the insights gained we hope to be able to understand and interpret better the results so obtained. PCA, as others “factor analysis” and Eigenvector Methods”, seeks to reveals the presumably simple underlying structure that might exist within a set of multivariate observations. This knowledge could help us to strengthen, supplement and validate the conclusions obtained from the traditional geochemical approach and can be considered a NDT tool for the characterization of alteration of geologic materials in the built environment as it does not involve the extraction of samples from those materials. The data set studied gathers information on seepage water samples collected over three years inside “Basilica da Estrela” (seepage waters derived from rainwater that penetrated and percolate the monument changing its composition through water-rock interactions). Precipitation of some of their dissolved components due saturation and/or evaporation along the monument percolating system contributed also for their final chemical and physical properties. Temperature, pH, electrical conductivity, SiO₂ and main ionic species were measured on each sample.