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# 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)

### See also

• lyap — Equation de Lyapunov
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