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 |
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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