## Abstract

Let GL_{m}(R) be the multiplicative group of C^{m×m} valued rational functions of one complex variable z with determinant not vanishing identically. We analyze general inner automorphisms of GL_{m}(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 language | English |
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Pages (from-to) | 531-566 |

Number of pages | 36 |

Journal | Linear Algebra and Its Applications |

Volume | 197-198 |

Issue number | C |

DOIs | |

State | Published - 1 Jan 1994 |

Externally published | Yes |

## ASJC Scopus subject areas

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