{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T22:03:35Z","timestamp":1759701815361},"reference-count":67,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,3,1]]},"abstract":"<jats:title>On generalized inverses of singular matrix pencils<\/jats:title><jats: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.<\/jats:p>","DOI":"10.2478\/v10006-011-0012-3","type":"journal-article","created":{"date-parts":[[2011,3,30]],"date-time":"2011-03-30T01:08:12Z","timestamp":1301447292000},"page":"161-172","source":"Crossref","is-referenced-by-count":6,"title":["On generalized inverses of singular matrix pencils"],"prefix":"10.61822","volume":"21","author":[{"given":"Klaus","family":"R\u00f6benack","sequence":"first","affiliation":[]},{"given":"Kurt","family":"Reinschke","sequence":"additional","affiliation":[]}],"member":"37438","reference":[{"issue":"8","key":"1","doi-asserted-by":"crossref","first-page":"1558","DOI":"10.1109\/TCSI.2004.832741","article-title":"Computation of singular and singularity induced bifurcation points of differential-algebraic power system model","volume":"51","author":"S. 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