A new equivalent condition of the reverse order law for G-inverses of multiple matrix products
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چکیده
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 the maximal rank of the generalized Schur complement, a new simpler equivalent condition is obtained in terms of only the ranks of the known matrices for this inclusion.
منابع مشابه
Ela a New Equivalent Condition of the Reverse Order Law for G-inverses of Multiple Matrix Products∗
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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تاریخ انتشار 2017