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See the recommended documentation of this function

# sylv

Sylvester equation.

### Syntax

`sylv(A, B, C, flag)`

### Arguments

A,B,C

three real matrices of appropriate dimensions.

flag

character string (`'c'` or `'d'`)

### Description

`X= sylv(A, B, C, 'c')` computes `X`, solution of the "continuous time" Sylvester equation

`A*X+X*B = C`

`X=sylv(A, B, C, 'd')` computes `X`, solution of the modified "discrete time" Sylvester equation

`A*X*B+X = C`

`X=-sylv(-A, B, C, 'd')` computes `X`, solution of the real "discrete time" Sylvester equation

`A*X*B-X = C`

### Examples

```// Continuous time Sylvester equation:
A = rand(4, 4); C = rand(4, 3); B = rand(3, 3);
X = sylv(A, B, C, 'c');
norm(A*X+X*B-C)

// Modified Discrete time Sylvester equation:
X = sylv(A, B, C, 'd');
norm(A*X*B+X-C)

// Real Discrete time Sylvester equation:
X = -sylv(-A, B, C, 'd');
norm(A*X*B-X-C)```