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This Letter deals with matrix extensions of the Fukui and dual-descriptor functions which are represented in a basis set by means of a spin-free treatment. A study of the eigenvalues of these matrices and of the values of the coefficients which express their eigenvectors provides important information concerning molecular reactivity. Numerical determinations performed in selected closed- and open-shell systems at Hartree-Fock and configuration interaction levels of theory show the usefulness of this procedure. A comparison between these results and those arising from other approaches is analyzed in detail.