In this article a fast computational method is provided in order to calculate the Moore-Penrose inverse of full rank m× n matrices and of square matrices with at least one zero row or column. Sufficient conditions are also given for special type products of square matrices so that the reverse order law for the Moore-Penrose inverse is satisfied.

In this work, we study the impact of the word order decoding direction for statistical machine translation (SMT). Both phrase-based and hierarchical phrasebased SMT systems are investigated by reversing the word order of the source and/or target language and comparing the translation results with the normal direction. Analysis are done on several components such as alignment model, language mod...

We prove that the (b, c)-inverse and inverse along an element in a semigroup are actually genuine when considered as morphisms Schützenberger category of semigroup. Applications to Reverse Order Law given.

We investigate some necessary and sufficient conditions for the hybrid reverse order law (ab) = b†a† in rings with involution. Assuming that a and b are Moore-Penrose invertible, we present equivalent condition for the product ab to be EP element.

In this paper, we use the Drazin inverse to derive some new equivalences of the reverse order law for the group inverse in unitary rings. Moreover, if the ring has an involution, we present more equivalences when both involved elements are EP.

In 1999, Wei [M.Wei, Reverse order laws for generalized inverse of multiple matrix products, Linear Algebra Appl., 293 (1999), pp. 273-288] studied reverse order laws for generalized inverses of multiple matrix products and derived some necessary and sufficient conditions for An{1}An−1{1} · · ·A1{1} ⊆ (A1A2 · · ·An){1} by using P-SVD (Product Singular Value Decomposition). In this paper, using ...

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We prove some identities related to the reverse order law for the Moore-Penrose inverse of operators on Hilbert spaces, extending some results from (Y. Tian and S. Cheng, Linear Multilinear Algebra 52 (2004)) and (R. E. Cline, SIAM Review, Vol. 6, No. 1 (1964)) to infinite dimensional settings. 2010 Mathematics Subject Classification: 47A05, 15A09.