On realization of left and right products of rational functions

Daniel Alpay, Izchak Lewkowicz

Research output: Contribution to journalArticlepeer-review


Let F(z) and G(z) be matrix-valued rational functions so that both product functions (FG)(z) and (GF)(z) are well defined. We here explore inter-relations between state-space realization of two pairs of functions: The original functions F and G, and on the other hand both of their products FG and GF. Motivated by the structure of asymmetric communication channels, we show how from the realization of the products FG and GF, one can explicitly recover the realizations of F and G.

Original languageEnglish
Pages (from-to)42-61
Number of pages20
JournalLinear Algebra and Its Applications
StatePublished - 1 Jun 2023


  • Factorization
  • Spectral factorization
  • State-space realization

ASJC Scopus subject areas

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


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