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On the Drazin index of regular elements

100%
Patrício P., Costa A.
Open Mathematics
|
2009
|
tom 7
|
nr 2
200-205
EN
It is known that the existence of the group inverse a # of a ring element a is equivalent to the invertibility of a 2 a − + 1 − aa −, independently of the choice of the von Neumann inverse a − of a. In this paper, we relate the Drazin index of a to the Drazin index of a 2 a − + 1 − aa −. We give an alternative characterization when considering matrices over an algebraically closed field. We close with some questions and remarks.
2
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Elements of C*-algebras commuting with their Moore-Penrose inverse

100%
Koliha J. J.
Studia Mathematica
|
2000
|
tom 139
|
nr 1
81-90
EN
We give new necessary and sufficient conditions for an element of a C*-algebra to commute with its Moore-Penrose inverse. We then study conditions which ensure that this property is preserved under multiplication. As a special case of our results we recover a recent theorem of Hartwig and Katz on EP matrices.
3
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On generalized inverses of singular matrix pencils

88%
Röbenack K., Reinschke K.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 1
161-172
EN
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 pencil and the multiplicity of poles at zero of the Moore-Penrose inverse and the Drazin inverse of the rational matrix are investigated. We present example networks whose circuit equations yield singular matrix pencils.
4
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Application of the Drazin inverse to the analysis of descriptor fractional discrete-time linear systems with regular pencils

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
|
tom 23
|
nr 1
29-33
EN
The Drazin inverse of matrices is applied to find the solutions of the state equations of descriptor fractional discrete-time systems with regular pencils. An equality defining the set of admissible initial conditions for given inputs is derived. The proposed method is illustrated by a numerical example.
5
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Analysis of the descriptor Roesser model with the use of the Drazin inverse

88%
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2015
|
tom 25
|
nr 3
539-546
EN
A method of analysis for a class of descriptor 2D discrete-time linear systems described by the Roesser model with a regular pencil is proposed. The method is based on the transformation of the model to a special form with the use of elementary row and column operations and on the application of a Drazin inverse of matrices to handle the model. The method is illustrated with a numerical example.
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