LyapunovSolve

LyapunovSolve[a,c] finds a solution x of the matrix Lyapunov equation a.x+x.aᵀ=c.

LyapunovSolve[a,b,c] solves a.x+x.bᵀ=c.

LyapunovSolve[{a,d},c] solves a.x.dᵀ+d.x.aᵀ=c.

LyapunovSolve[{a,d},{b,e},c] solves a.x.eᵀ+d.x.bᵀ=c.

Examples

Solve a Lyapunov equation:

LyapunovSolve[{{1, 2}, {0, 3}}, {{1, 0}, {0, 1}}]
(* {{1/2, 1/5}, {1/5, 1/6}} *)

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