Ela Rank and Inertia of Submatrices of the Moore–penrose Inverse of a Hermitian Matrix

Rank and inertia of submatrices of the Moore-Penrose inverse of a Hermitian matrix

Investigation on the Hermitian matrix expression‎ ‎subject to some consistent equations

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...

Ela New Representations for the Moore-penrose Inverse

In this paper, some new representations of the Moore-Penrose inverse of a complex m × n matrix of rank r in terms of (s × t)-constrained submatrices with m ≥ s ≥ r, n ≥ t ≥ r are presented.

Hermitian solutions to the system of operator equations T_iX=U_i.

In this article we consider the system of operator equations T_iX=U_i for i=1,2,...,n and give necessary and suffcient conditions for the existence of common Hermitian solutions to this system of operator equations for arbitrary operators without the closedness condition. Also we study the Moore-penrose inverse of a ncross 1 block operator matrix and. then gi...

An Efficient Schulz-type Method to Compute the Moore-Penrose Inverse

A new Schulz-type method to compute the Moore-Penrose inverse of a matrix is proposed. Every iteration of the method involves four matrix multiplications. It is proved that this method converge with fourth-order. A wide set of numerical comparisons shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods.