Thomas L. Markham

A Generalization of the Schur Complement by Means of the Moore–Penrose Inverse

Suppose the complex matrix M is partitioned into a

Completing a matrix when certain entries of its inverse are specified

2 \times 2

Generalized Inverse Formulas Using the Schur Complement

array of blocks; let

Convergence of a direct-iterative method for large-scale least-squares problems

M_{11} = A,M_{12} = B,M_{21} = C,M_{22} = D

An inequality for the hadamard product of an M-matrix and an inverse M-matrix

. The generalized Schur complement of A in M is defined to be

A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix

M/A = D - CA^ + B

The Moore-Penrose inverse of a partitioned matrix M=(ADBC)

, where

Factorizations of completely positive matrices

A^ +

Consecutive-column and -row properties of matrices and the loewner-neville factorization

is the Moore–Penrose inverse of A. The relationship of the ranks of M, A, and

A characterization of the Moore-Penrose inverse

M/A