## Abstract

Natural connections between positive semidefinite solutions X of homogeneous algebraic Riccati equations and finite dimensional reproducing kernel de Branges spaces based on a J-inner proper rational square matrix valued functions are known. In this paper analogous connections between the positive semidefinite solutions X of nonhomogeneous algebraic Riccati equations and finite dimensional reproducing kernel Hilbert spaces based on rectangular (J, over(J, ∼))-coinner proper rational matrix valued functions Θ(λ) are developed and are then applied to obtain factorization formulas for Θ(λ) in terms of elementary factors. Enroute, formulas for the factors in a version of a theorem of Leech are also obtained.

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

Pages (from-to) | 458-482 |

Number of pages | 25 |

Journal | Linear Algebra and Its Applications |

Volume | 420 |

Issue number | 2-3 |

DOIs | |

State | Published - 15 Jan 2007 |

Externally published | Yes |

## Keywords

- Factorization
- Nonhomogeneous Riccati equations
- Rectangular (J, over(J, ∼))-coinner matrix valued functions
- Reproducing kernels

## ASJC Scopus subject areas

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