Ela Schur Complements and Banachiewicz - Schur Forms
نویسندگان
چکیده
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.
منابع مشابه
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 کاملEla Generalized Schur Complements of Matrices and Compound Matrices
In this paper, we obtain some formulas for compound matrices of generalized Schur complements of matrices. Further, we give some Löwner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of Schur complements of sums of positive semidefinite Hermitian matrices.
متن کاملEla Schur Complements of Generally Diagonally Dominant Matrices and a Criterion for Irreducibility of Matrices∗
As is well known, the Schur complements of strictly or irreducibly diagonally dominant matrices are H−matrices; however, the same is not true of generally diagonally dominant matrices. This paper proposes some conditions on the generally diagonally dominant matrix A and the subset α ⊂ {1, 2, . . . , n} so that the Schur complement matrix A/α is an H−matrix. These conditions are then applied to ...
متن کاملEla Nonnegativity of Schur Complements of Nonnegative
Let A be a nonnegative idempotent matrix. It is shown that the Schur complement of a submatrix, using the Moore-Penrose inverse, is a nonnegative idempotent matrix if the submatrix has a positive diagonal. Similar results for the Schur complement of any submatrix of A are no longer true in general.
متن کاملFormulae for the generalized Drazin inverse of a block matrix in terms of Banachiewicz–Schur forms
We introduce new expressions for the generalized Drazin inverse of a block matrix with the generalized Schur complement being generalized Drazin invertible in a Banach algebra under some conditions. We generalized some recent results for Drazin inverse and group inverse of complex matrices.
متن کامل