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Factorization of positive definite rational matrix functions

  • Harm Bart
  • Marinus A. Kaashoek
  • André C. M. Ran
Part of the Operator Theory: Advances and Applications book series (OT, volume 200)

Abstract

The central theme of this chapter is the state space analysis of rational matrix functions with Hermitian values either on the real line, on the imaginary axis, or on the unit circle. The main focus will be on rational matrix functions that take positive definite values on one of these contours. It will be shown that if W is such a function, then W admits a spectral factorization, i.e., a canonical factorization W=WW+ with an additional symmetry between the corresponding factors, depending on the contour.

Keywords

Unit Circle Real Line Matrix Function Half Plane Imaginary Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser/Springer Basel AG 2010

Authors and Affiliations

  • Harm Bart
    • 1
  • Marinus A. Kaashoek
    • 2
  • André C. M. Ran
    • 2
  1. 1.Econometrisch InstituutErasumus Universiteit RotterdamRotterdamThe Netherlands
  2. 2.Department of Mathematics, FEWVrije UniversiteitAmsterdamThe Netherlands

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