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Latent Semantic Analysis (LSA) is based on the Singular Value Decomposition (SVD) of a term-by-document matrix for identifying relationships among terms and documents from cooccurrence patterns. Among the multiple ways of computing the SVD of a rectangular matrix X, one approach is to compute the eigenvalue decomposition (EVD) of a square 2 x 2 composite matrix consisting of four blocks with X and XT in the off-diagonal blocks and zero matrices in the diagonal blocks. We point out that significant value can be added to LSA by filling in some of the values in the diagonal blocks (corresponding to explicit term-to-term or document-to-document associations) and computing a term-by-concept matrix from the EVD. For the case of multilingual LSA, we incorporate information on cross-language term alignments of the same sort used in Statistical Machine Translation (SMT). Since all elements of the proposed EVD-based approach can rely entirely on lexical statistics, hardly any price is paid for the improved empirical results. In particular, the approach, like LSA or SMT, can still be generalized to virtually any language(s); computation of the EVD takes similar resources to that of the SVD since all the blocks are sparse; and the results of EVD are just as economical as those of SVD.