<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

On generalized inverses of singular matrix pencils

Institute of Control Theory Faculty of Electrical and Computer Engineering, Technische Universität Dresden, D-01062 Dresden, Germany

International Journal of Applied Mathematics and Computer Science

{"article-title":"On generalized inverses of singular matrix pencils"}

Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a...

On generalized inverses of singular matrix pencils

Published Online: Mar 28, 2011

Page range: 161 - 172

DOI: https://doi.org/10.2478/v10006-011-0012-3

Keywords
matrix pencils, Kronecker indices, Moore-Penrose inverse, Drazin inverse, linear networks

This content is open access.

On generalized inverses of singular matrix pencils

Published Online: Mar 28, 2011

Page range: 161 - 172

DOI: https://doi.org/10.2478/v10006-011-0012-3

Keywordsmatrix pencils, Kronecker indices, Moore-Penrose inverse, Drazin inverse, linear networks

This content is open access.

Keywords
matrix pencils, Kronecker indices, Moore-Penrose inverse, Drazin inverse, linear networks