Ela 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
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 ...
متن کاملEla a Note on the Reverse Order Laws for {1, 2, 3}- and {1, 2, 4}-inverses of Multiple Matrix Products
Abstract. Motivated by the equivalent conditions for the inclusions An{1, 2, i} · · ·A2{1, 2, i}A1{1, 2, i} ⊆ (A1A2 · · ·An){1, 2, i} (i = 3, 4) presented in [B. Zheng and Z. Xiong. The reverse order laws for {1,2,3}and {1,2,4}-inverses of multiple matrix products. Linear Multilinear Algebra, 58:765–782, 2010.], we show that for i ∈ {3, 4}, An{1, 2, i} · · ·A2{1, 2, i}A1{1, 2, i} = (A1A2 · · ·A...
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Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...
متن کاملEla the Reverse Order Laws and the Mixed-type Reverse Order Laws for Generalized Inverses of Multiple Matrix Products
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تاریخ انتشار 2008