## Abstract

We show that a polynomial p with no zeros on the closure of a matrix unit polyball, a.k.a. a cartesian product of Cartan domains of type I, and such that (Formula presented.) , admits a strictly contractive determinantal representation, i.e., (Formula presented.) , where (Formula presented.) is a k-tuple of nonnegative integers, (Formula presented.) , (Formula presented.) are complex matrices, p is a polynomial in the matrix entries (Formula presented.) , and K is a strictly contractive matrix. This result is obtained via a noncommutative lifting and a theorem on the singularities of minimal noncommutative structured system realizations.

Original language | English |
---|---|

Pages (from-to) | 25-37 |

Number of pages | 13 |

Journal | Mathematische Zeitschrift |

Volume | 283 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Jun 2016 |

## Keywords

- Classical Cartan domain
- Contractive determinantal representation
- Contractive realization
- Polyball
- Stable polynomial
- Structured noncommutative multidimensional system

## ASJC Scopus subject areas

- General Mathematics