The drazin inverse through the matrix pencil approach and its application to the study of generalized linear systems with rectangular or square coefficient matrices

Grigoris I. Kalogeropoulos, Athanasios D. Karageorgos, Athanasios A. Pantelous

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3 Citations (Scopus)

Abstract

In several applications, e.g., in control and systems modeling theory, Drazin inverses and matrix pencil methods for the study of generalized (descriptor) linear systems are used extensively. In this paper, a relation between the Drazin inverse and the Kronecker canonical form of rectangular pencils is derived and fully investigated. Moreover, the relation between the Drazin inverse and the Weierstrass canonical form is revisited by providing a more algorithmic approach. Finally, the Weierstrass canonical form for a pencil through the core-nilpotent decomposition method is defined.

Original languageEnglish
Pages (from-to)118-138
Number of pages21
JournalElectronic Journal of Linear Algebra
Volume17
Publication statusPublished - Mar 2008
Externally publishedYes

Keywords

  • Drazin inverse
  • Generalized linear systems
  • Matrix pencil theory

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