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Carlo Beenakker
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This is the Sylvester equation. A simple explicit solution is possible under certain conditions (no common eigenvalues of the matrices $C^{-1}A$ and $-DB^{-1}$), as explained in the Wikipedia page. There are more complicated general methods, see

  1. Explicit solutions of the matrix equation $AX−XB=C$ (1974)
  2. The explicit solution of the matrix equation $AX−XB=C$ (1995)
  3. Continued-fraction solution of matrix equation $AX-XB=C$(1989)
  4. Explicit solutions of the matrix equation $AX−XB=C$ (1974)
  5. Explicit Solutions of Linear Matrix Equations (1970)

This is the Sylvester equation. A simple explicit solution is possible under certain conditions (no common eigenvalues of the matrices $C^{-1}A$ and $-DB^{-1}$), as explained in the Wikipedia page. There are more complicated general methods, see

  1. Explicit solutions of the matrix equation $AX−XB=C$ (1974)
  2. The explicit solution of the matrix equation $AX−XB=C$ (1995)
  3. Continued-fraction solution of matrix equation $AX-XB=C$(1989)

This is the Sylvester equation. A simple explicit solution is possible under certain conditions (no common eigenvalues of the matrices $C^{-1}A$ and $-DB^{-1}$), as explained in the Wikipedia page. There are more complicated general methods, see

  1. The explicit solution of the matrix equation $AX−XB=C$ (1995)
  2. Continued-fraction solution of matrix equation $AX-XB=C$(1989)
  3. Explicit solutions of the matrix equation $AX−XB=C$ (1974)
  4. Explicit Solutions of Linear Matrix Equations (1970)
Source Link
Carlo Beenakker
  • 188.1k
  • 18
  • 448
  • 651

This is the Sylvester equation. A simple explicit solution is possible under certain conditions (no common eigenvalues of the matrices $C^{-1}A$ and $-DB^{-1}$), as explained in the Wikipedia page. There are more complicated general methods, see

  1. Explicit solutions of the matrix equation $AX−XB=C$ (1974)
  2. The explicit solution of the matrix equation $AX−XB=C$ (1995)
  3. Continued-fraction solution of matrix equation $AX-XB=C$(1989)