A special structure of a kind of matrices, r−block monomial and r−block diagonal matrices, is introduced. Theirs nonnegative Drazin inverses have been studied. The influence of these matrices on the positiveness of the trajectory of a descriptor system has been analyzed. Key–Words:Drazin inverse, nonnegative matrix, block monomial matrix, descriptor system.

In this paper we give representations of the Drazin and MP-inverse of a 2×2 block matrix and quotient identities for the generalized Schur complement of a partitioned 3 × 3 matrix under conditions different than those used in recent papers on the subject. We present numerical examples to illustrate our results. 2000 Mathematics Subject Classification: 15A09

In this paper we define and study a generalized Drazin inverse x for ring elements x, and give a characterization of elements a, b for which aa = bb. We apply our results to the study of EP elements in a ring with involution. 2000 Mathematics subject classification: primary 16A32, 16A28, 15A09; secondary 46H05, 46L05.

This paper deals with the algorithm for computing outer inverse with prescribed range and null space, based on the choice of an appropriate matrix G and Gauss–Jordan elimination of the augmented matrix [G | I]. The advantage of such algorithms is the fact that one can compute various generalized inverses using the same procedure, for different input matrices. In particular, we derive representa...

In this paper, we give a generalized Cline?s formula for the Drazin inverse. Let R be ring, and let a, b, c, d ? satisfying (ac)2 = (db)(ac), (db)2 (ac)(db), b(ac)a b(db)a, c(ac)d c(db)d. Then ac Rd if only bd Rd. case, (bd)d b((ac)d)2d: We also present formulas group inverses. Some weaker conditions in Banach algebra are investigated. These extend main results of on g-Drazin inverse Liao, Chen...

Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate s...