is called the Drazin inverse of A and is denoted by X = A, where k is the index of A, i.e., the smallest non-negative integer such that rank(A) = rank(A). We denote such a k by Ind(A). It is well-known that A exists and is unique (see [2]). If Ind(A) = 1, A is also called the group inverse of A and is denoted by A. Then A exists if and only if rank(A) = rank(A) (see [1, 3, 11-14, 24, 25, 29]). ...

In this paper we introduce an interpolation method for computing the Drazin inverse of a given polynomial matrix. This method is an extension of the known method from [15], applicable to usual matrix inverse. Also, we improve our interpolation method, using a more effective estimation of degrees of polynomial matrices generated in Leverrier-Faddev method. Algorithms are implemented and tested i...

In this paper, we give explicit expressions of (P ± Q)d of two matrices P and Q, in terms of P, Q, Pd and Qd, under the condition that PQ = P 2, and apply the result to finding an explicit representation for the Drazin inverse of a 2×2 block matrix [ A B C D ] under some conditions.

The purpose of this paper is to introduce and study a new class operators that we call pseudogeneralized invertible operators. This includes both the generalized Drazin Some results connected with ascent essential are also obtained for class. relationship between pseudo-generalized operators, semi-Fredholm explored.

The generalized null space decomposition (GNSD) is a unitary reduction of a general matrix A of order n to a block upper triangular form that reveals the structure of the Jordan blocks of A corresponding to a zero eigenvalue. The reduction was introduced by Kublanovskaya. It was extended first by Ruhe and then by Golub and Wilkinson, who based the reduction on the singular value decomposition. ...

In a recent work by the author [Linear Algebra Appl. 298 (1999) 99] Krylov subspace methods were derived for the Drazin-inverse solution of consistent or inconsistent linear systems of the form Ax = b, where A ∈ CN×N is a singular and in general non-hermitian matrix that has an arbitrary index. One of these methods, modeled after the generalized conjugate residual method (GCR) and denoted DGCR,...