# sylvester

sylvester(A, B, C)

Computes the solution `X`

to the Sylvester equation `AX + XB + C = 0`

, where `A`

, `B`

and `C`

have compatible dimensions and `A`

and `-B`

have no eigenvalues with equal real part.

## Examples

```
julia> A = [1 2; 3 4];
julia> B = [5 6; 7 8];
julia> C = [9 10; 11 12];
julia> X = sylvester(A, B, C)
2×2 Array{Float64,2}:
-1.5 -1.75
-2.5 -2.75
```

This example demonstrates how to use the `sylvester`

function to solve the Sylvester equation `AX + XB + C = 0`

. The matrices `A`

, `B`

, and `C`

are provided as inputs, and the function returns the solution matrix `X`

.

Note that the dimensions of `A`

, `B`

, and `C`

must be compatible for the equation to be solvable. Additionally, `A`

and `-B`

must not have any eigenvalues with equal real parts.

It's important to ensure that the matrices provided are of the correct dimensions and satisfy the required conditions for the Sylvester equation.

## See Also

## User Contributed Notes

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