Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero

González, N. Castro; Koliha, J. J.; Wei, Yimin

doi:10.1016/s0024-3795(00)00101-4

Cited by 57 publications

(44 citation statements)

References 7 publications

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“…For two given matrices A, B ∈ C n 0 ∪ C n 1 , necessary and sufficient conditions for the equality f (A) = f (B) to be satisfied are given in [9,11]. Some results about inequalities are given below.…”

Section: On the Eigenprojection Atmentioning

confidence: 99%

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The star partial order and the eigenprojection at 0 on EP matrices

Hernández

Lattanzi

Thome

et al. 2012

Applied Mathematics and Computation

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The star partial order and the eigenprojection at 0 on EPThe space of n × n complex matrices with the star partial order is considered in the first part of this paper. The class of EP matrices is analyzed and several properties related to this order are given. In addition, some information about predecessors and successors of a given EP matrix is obtained. The second part is dedicated to the study of some properties that relate the eigenprojection at 0 with the star and sharp partial orders.

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Section: On the Eigenprojection Atmentioning

confidence: 99%

“…In [9,10,11,12], the authors worked with the concept of eigenprojection at 0. Specifically, for A ∈ C n×n of index at most 1, it is possible to define its eigenprojection at 0 as A π = I −AA # , which is the projection onto N (A) along R(A).…”

Section: Introductionmentioning

confidence: 99%

The star partial order and the eigenprojection at 0 on EP matrices

Hernández

Lattanzi

Thome

et al. 2012

Applied Mathematics and Computation

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“…Also, the Drazin inverse perturbation theory has been studied from different points of view. For instance, in [8,37] algebraic approaches has been given while a setting in systems theory can be found in [4,35,36].…”

Section: Introductionmentioning

confidence: 99%

An algorithm to study the nonnegativity, regularity and stability via state-feedbacks of singular systems of arbitrary index

Herrero

Ramı́rez

Thome

2014

Linear and Multilinear Algebra

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This paper deals with singular systems of index k ≥ 1. Our main goal is to find a state-feedback such that the closed-loop system satisfies the regularity condition and it is nonnegative and stable. In order to do that, the core-nilpotent decomposition of a square matrix is applied to the singular matrix of the system. Moreover, if the Drazin projector of this matrix is nonnegative then the previous decomposition allows us to write the core-part of the matrix in a specific block form. In addition, an algorithm to study this kind of systems via a state-feedback is designed.

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“…A particular case is when the matrix B satisfies The class of perturbation matrices B related to A by the condition (1.1), which is equivalent to the fact that both matrices have equal eigenprojection at zero, B π = A π with A π = I − AA D , were characterized in [4]. The Drazin inverse of B satisfying (1.1) is given by the formula B D = (I + A D (B − A)) −1 A D .…”

Section: Introduction and Preliminaries Let A ∈ Cmentioning

confidence: 99%

“…This latter formula was given in [15] for B = A + E, where E = AA D EAA D and E sufficiently small. The first and third authors gave in [5] [4,5,6,8,9,12,13,14,15,16].…”

Section: Introduction and Preliminaries Let A ∈ Cmentioning

confidence: 99%