The purpose of this paper is to introduce a new generalized inverse, called DMP inverse, associated with a square complex matrix using its Drazin and Moore-Penrose inverses. DMP inverse extends the notion of core inverse, introduced by O.M. Baksalary and G. Trenkler for matrices of index at most 1 in [Core inverse of matrices, Linear and Multilinear Algebra, 2010, 681–697] to matrices of an arb...

A simple formula for the group inverse of a 2× 2 block matrix with a bipartite digraph is given in terms of the block matrices. This formula is used to give a graph-theoretic description of the group inverse of an irreducible tridiagonal matrix of odd order with zero diagonal (which is singular). Relations between the zero/nonzero structures of the group inverse and the Moore-Penrose inverse of...

We study the spectrum and the rank of a linear combination of two orthogonal projectors. We characterize when this linear combination is EP, diagonalizable, idempotent, tripotent, involutive, nilpotent, generalized projector, and hypergeneralized projector. Also we derive the Moore-Penrose inverse of a linear combination of two orthogonal projectors in a particular case. The main tool used here...

We modify the algorithm of [1], based on Newton’s iteration and on the concept of 2-displacement rank, to the computation of the Moore-Penrose inverse of a rank-deficient Toeplitz matrix. Numerical results are presented to illustrate the effectiveness of the method.

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.

We introduce some new algebraic and topological properties of the Minkowski inverse A([Symbol: see text) of an arbitrary matrix A[Symbol: see text] M m,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A ([Symbol: see text]) in a Minkowski space and the Moore-Penrose inverse A(+) in a Hilbert space are different in many properties suc...

We consider here the problem of estimating p×p scale matrix Σ a multivariate linear regression model when distribution observed belongs to large class elliptically symmetric distributions. Any estimator Σˆ is assessed through data-based loss tr(S+Σ(Σ−1Σˆ−Ip)2) where S sample covariance and S+ its Moore–Penrose inverse.

A connected signed graph Ġ, where all blocks of it are positive cliques or negative (of possibly varying sizes), is called a block graph. Let A, N and D̃ be adjacency, net Laplacian distance matrices graph, respectively. In this paper the formulas for determinant were given firstly. Then inverse (resp. Moore-Penrose inverse) obtained if nonsingular singular), which sum Laplacian-like matrix at m...

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory generalized within algebraic structure a ring. In this paper, we study different over commutative ring noncommutative Several examples are provided support theoretical results. We also propose algorithms for computing inner inverses, Moor...

We introduce a method and algorithm for computing the weighted MoorePenrose inverse of multiple-variable polynomial matrix and the related algorithm which is appropriated for sparse polynomial matrices. These methods and algorithms are generalizations of algorithms developed in [24] to multiple variable rational and polynomial matrices and improvements of these algorithms on sparse matrices. Al...