# lyap

lyap(A, C)

Computes the solution `X`

to the continuous Lyapunov equation `AX + XA' + C = 0`

, where no eigenvalue of `A`

has a zero real part and no two eigenvalues are negative complex conjugates of each other.

## Examples

```
julia> A = [1 2; 3 4];
julia> C = [5 6; 7 8];
julia> X = lyap(A, C)
2×2 Array{Float64,2}:
-32.0 -44.0
-52.0 -72.0
```

In this example, the `lyap`

function computes the solution `X`

to the continuous Lyapunov equation `AX + XA' + C = 0`

, where `A`

is a 2x2 matrix and `C`

is another 2x2 matrix.

The function returns the resulting matrix `X`

, which satisfies the Lyapunov equation.

Note: The specific values in the example are arbitrary and provided for demonstration purposes. The actual values will depend on the input matrices `A`

and `C`

.

## See Also

Ac_ldiv_B, Ac_ldiv_Bc, Ac_mul_B, Ac_mul_Bc, Ac_rdiv_B, Ac_rdiv_Bc, At_ldiv_B, At_ldiv_Bt, At_mul_B, At_mul_Bt, At_rdiv_B, At_rdiv_Bt, A_ldiv_Bc, A_ldiv_Bt, A_mul_B!, A_mul_Bc, A_mul_Bt, A_rdiv_Bc, A_rdiv_Bt, Bidiagonal, cond, conv2, det, diag, diagind, diagm, diff, eig, eigvals, eigvecs, expm, eye, full, inv, isdiag, ishermitian, isposdef, isposdef!, issym, istril, istriu, logabsdet, logdet, lyap, norm, qrfact, rank, repmat, rot180, rotl90, rotr90, sortrows, sqrtm, SymTridiagonal, trace, Tridiagonal, tril, tril!, triu, triu!, writedlm,## User Contributed Notes

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