J-unitary preserving automorphisms of rational matrix functions: state space theory, interpolation, and factorization

Daniel Aron Alpay, Joseph A. Ball, Israel Gohberg, Leiba Rodman

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Let GLm(R) be the multiplicative group of Cm×m valued rational functions of one complex variable z with determinant not vanishing identically. We analyze general inner automorphisms of GLm(R) that preserve the set of matrix functions whose values are unitary (with respect to an indefinite scalar product) for real, or unimodular, values of z. The analysis is based on state space representations. In particular, homogeneous interpolation problems are studied for the rational matrix functions associated with such a general inner automorphism. We also develop results on minimal factorizations within the group associated with J-unitary preserving generalized inner automorphism.

Original languageEnglish
Pages (from-to)531-566
Number of pages36
JournalLinear Algebra and Its Applications
Volume197-198
Issue numberC
DOIs
StatePublished - 1 Jan 1994
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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