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I want to solve

$$X \cdot A + A^T = I$$

for $X$, $A$ and $X$ are arbitrary matrices and $A$ is invertible. I know that $A \cdot A^{-1} = I$, this helps, but I don't know how to deal with the additional $+A^T$.

How can I approach this?

  • 0
    Did you mean "$A$ is invertible" in your hypothesis instead of "$X$ is invertible"?2012-04-13
  • 0
    Yes, sorry for the typo; $A$ is invertible2012-04-13
  • 0
    @Mahoni, solutions remains the same, false assumption that I made before was that A must be invertible to solve it2012-04-13

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