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This question is about equations where the unknown itself is a matrix such as Sylvester or Riccati equations. For systems of linear equations (where the unknown is a vector), use "linear-system".

8 votes

Compute $x = B^{-1}(2A+I)(C^{-1}+A)b$ without calculating matrix inverses

As was mentioned in the comment, calculating $x=M^{-1}y$ is equivalent to solving $Mx=y$. Here is the full solution: First, you can reformulate the equation to: $Bx=(2A+I)(C^{-1}+A)b$, and by defini …
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