New Representations of the Group Inverse of2×2Block Matrices

New Representations of the Group Inverse of 2×2 Block Matrices

This paper presents a full rank factorization of a 2 × 2 block matrix without any restriction concerning the group inverse. Applying this factorization, we obtain an explicit representation of the group inverse in terms of four individual blocks of the partitioned matrix without certain restriction. We also derive some important coincidence theorems, including the expressions of the group inver...

Ela a Note on Block Representations of the Group Inverse of Laplacian Matrices

Let G be a weighted graph with Laplacian matrix L and signless Laplacian matrix Q. In this note, block representations for the group inverse of L and Q are given. The resistance distance in a graph can be obtained from the block representation of the group inverse of L.

Representations and sign pattern of the group inverse for some block matrices

Let M= ( A B C 0 ) be a complex square matrix where A is square. When BCB = 0, rank(BC) = rank(B) and the group inverse of ( BAB 0 CB 0 ) exists, the group inverse of M exists if and only if rank(BC + A ( BAB ) π BA) = rank(B). In this case, a representation of M in terms of the group inverse and Moore-Penrose inverse of its subblocks is given. Let A be a real matrix. The sign pattern of A is a...

Representations for the Drazin inverse of block cyclic matrices

Ela Representations for the Drazin Inverse of Block Cyclic Matrices

REPRESENTATIONS FOR THE DRAZIN INVERSE OF BLOCK CYCLIC MATRICES M. CATRAL AND P. VAN DEN DRIESSCHE Abstract. A formula for the Drazin inverse of a block k-cyclic (k ≥ 2) matrix A with nonzeros only in blocks Ai,i+1, for i = 1, . . . , k (mod k) is presented in terms of the Drazin inverse of a smaller order product of the nonzero blocks of A, namely Bi = Ai,i+1 · · ·Ai−1,i for some i. Bounds on ...