Eikonal Blog

2010.10.14

Sylvester and Lyapunov equations

Definitions: ([1],[2]) For n\times n matrices A, B, X, Y:

  • the Sylvester equation: AY+YB=X;
  • the Lyapunov equation: AYA^{\dagger}-Y=X;
  • the “continuous” Lyapunov equation: AY+YA^{\dagger}=X.

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