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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
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When does this linear matrix equation have a unique symmetric, positive definite solution?
I encountered the following matrix equation for $A, N, Q \in \mathbb{R}^{n \times n}$ and $A^T=-A$ and $N^T=-N$
$$[X,A]+N^TXN+Q = 0$$
where $Q$ is symmetric, positive definite. My final goal is to …