Representations of generalized inverses of partitioned matrix involving Schur complement
نویسندگان
چکیده
In this article, we consider some representations of {1, 3}, {1, 4}, {1, 2, 3} and {1, 2, 4}-inverses of a partitioned matrix M which are equivalent to some rank additivity conditions. We present some applications of these results to generalizations of the Sherman-Morrison-Woodbury-type formulae.
منابع مشابه
Ela Schur Complements and Banachiewicz - Schur Forms
Through the matrix rank method, this paper gives necessary and sufficient conditions for a partitioned matrix to have generalized inverses with Banachiewicz-Schur forms. In addition, this paper investigates the idempotency of generalized Schur complements in a partitioned idempotent matrix.
متن کاملSchur complements and Banachiewicz-Schur forms
Through the matrix rank method, this paper gives necessary and sufficient conditions for a partitioned matrix to have generalized inverses with Banachiewicz-Schur forms. In addition, this paper investigates the idempotency of generalized Schur complements in a partitioned idempotent matrix.
متن کاملGeneralized Drazin inverse of certain block matrices in Banach algebras
Several representations of the generalized Drazin inverse of an anti-triangular block matrix in Banach algebra are given in terms of the generalized Banachiewicz--Schur form.
متن کاملExpression of the Drazin and MP-inverse of partitioned matrix and quotient identity of generalized Schur complement
In this paper we give representations of the Drazin and MP-inverse of a 2×2 block matrix and quotient identities for the generalized Schur complement of a partitioned 3 × 3 matrix under conditions different than those used in recent papers on the subject. We present numerical examples to illustrate our results. 2000 Mathematics Subject Classification: 15A09
متن کاملA 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 219 شماره
صفحات -
تاریخ انتشار 2013