Displaying similar documents to “The Drazin inverse through the matrix pencil approach and its application to the study of generalized linear systems with rectangular or square coefficient matrices.”

Some equalities for generalized inverses of matrix sums and block circulant matrices

Yong Ge Tian (2001)

Archivum Mathematicum

Similarity:

Let A 1 , A 2 , ⋯ , A n be complex matrices of the same size. We show in this note that the Moore-Penrose inverse, the Drazin inverse and the weighted Moore-Penrose inverse of the sum ∑ t = 1 n A t can all be determined by the block circulant matrix generated by A 1 , A 2 , ⋯ , A n . In addition, some equalities are also presented for the Moore-Penrose inverse and the Drazin inverse of a quaternionic matrix.

Positive splittings of matrices and their nonnegative Moore-Penrose inverses

Tamminana Kurmayya, Koratti C. Sivakumar (2008)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

In this short note we study necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a real matrix in terms of certain spectral property shared by all positive splittings of the given matrix.

Intervals of certain classes of Z-matrices

M. Rajesh Kannan, K.C. Sivakumar (2014)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

On generalized inverses of singular matrix pencils

Klaus Röbenack, Kurt Reinschke (2011)

International Journal of Applied Mathematics and Computer Science

Similarity:

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 singular matrix pencils. The relations between the Kronecker structure of a singular matrix...