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LyapunovSolve

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Solves a.x + x.aT == c (3-arg Sylvester a.x + x.b == c) exactly for real numeric matrices; diagonal symbolic a gives Conjugate closed forms

LyapunovSolve[a, c]
LyapunovSolve[a, b, c]
LyapunovSolve[{a, d}, c]
LyapunovSolve[{a, d}, {b, e}, c]
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