“…The query intersects the TDM at the first and last documents, and as mentioned before the TDM is diagonal and therefore the S matrix is also diagonal, and so removing any elements from the diagonal values results in removing the same diagonal values in the original TDM. Thus, when the SVD is applied at the range of k−values (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14), only the first document is returned, because at this range of values the last document, which is document number 15, is ignored. It is important to note that, applying the LSI at k − value 15, which means no dimension reduction occurs, returns the two documents, the first and the last documents in the TDM, which have a cosine value of 0.7071.…”