کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4602882 | 1631178 | 2007 | 7 صفحه PDF | دانلود رایگان |

In 1979, Campbell and Meyer proposed the problem of finding a formula for the Drazin inverse of a 2 × 2 matrix in terms of its various blocks, where the blocks A and D are required to be square matrices. Special cases of the problems have been studied. In particular, a representation of the Drazin inverse of M, denoted by MD, has recently been obtained under the assumptions that C(I − AAD)B = O and A(I − AAD)B = O together with the condition that the generalized Schur complement D − CADB be either nonsingular or zero. We derive an alternative representation for MD under the same assumptions, but with the condition on the Schur complement in the hypothesis replaced by the condition that R(CAAD)⊂N(B)∩N(D), where R(·) and N(·) are the range and null space of a matrix.
Journal: Linear Algebra and its Applications - Volume 423, Issues 2–3, 1 June 2007, Pages 332-338