The study of the projective transformation under the bilinear strict equivalence

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

Research output: Contribution to journalArticleResearchpeer-review


The study of linear time invariant descriptor systems has intimately been related to the study of matrix pencils. It is true that a large number of systems can be reduced to the study of differential (or difference) systems, S(F,G)⁠,

S(F,G):Fx˙(t)=Gx(t)(or the dual, Fx(t)=Gx˙(t)),


S(F,G):Fxk+1=Gxk(or the dual, Fxk=Gxk+1),F,G∈Cm×n,

and their properties can be characterized by homogeneous matrix pencils, sF−s^G⁠. Based on the fact that the study of the invariants for the projective equivalence class can be reduced to the study of the invariants of the matrices of set Ck×2 (for k⩾3 with all 2×2-minors non-zero) under the extended Hermite equivalence, in the context of the bilinear strict equivalence relation, a novel projective transformation is analytically derived.

Original languageEnglish
Pages (from-to)383-408
Number of pages26
JournalIMA Journal of Mathematical Control and Information
Issue number2
Publication statusPublished - Jun 2022


  • bilinear-strict equivalence
  • extended Hermite Equivalence
  • linear systems
  • matrix pencil theory

Cite this