Positive Linear Maps and the Lyapunov Equation

  • Rajendra Bhatia
  • Ludwig Elsner
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 130)


It is well-known that positivity plays an important role in the study of the discrete time and the continuous time Lyapunov equations. We show how general theorems on positive linear maps on matrices may be used in this context. Our method leads to several old, recent, and new bounds on the sensitivity of these equations. Further, it can be applied to related problems and to other matrix equations as well.


Linear Algebra Matrix Equation Operator Algebra Open Unit Disk Lyapunov Equation 
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

© Springer Basel AG 2002

Authors and Affiliations

  • Rajendra Bhatia
    • 1
  • Ludwig Elsner
    • 2
  1. 1.Delhi Center, 7, S.J.S. Sansanwal MargIndian Statistical InstituteNew DelhiIndia
  2. 2.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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