The purpose of this study is to propose a simple technique based on matrix algebra to compute the Gini Index of Inequality, to obtain a decomposition of this index by factor components, when detailed data on the various income sources are available, to derive a breakdown of the inequality into within and between classes inequality, when the income units are grouped by income range, and to compute the contribution of the within and between groups inequality as well as that of some interaction term, when the data are classified by population subgroups.