Sur l'intersectiondes noyaux des opérateurs de matrices pour les séries formelles non commutatives

Translated title of the contribution: On the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series

Daniel Alpay, Dmitry S. Kalyuzhnyǐ-Verbovetzkiǐ

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

For a rational formal power series in N non-commuting indeterminates, with matrix coefficients, we establish the formula which relates the intersection of the null spaces of coefficients to the intersection of the null spaces of values of this series at N-tuples of n × n matrices, for n large enough. As an application, we formulate the criteria of observability, controllability, and minimality for a recognizable formal power series representation in terms of matrix substitutions.

Translated title of the contributionOn the intersection of null spaces for matrix substitutions in a non-commutative rational formal power series
Original languageFrench
Pages (from-to)533-538
Number of pages6
JournalComptes Rendus Mathematique
Volume339
Issue number8
DOIs
StatePublished - 15 Oct 2004

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