 Home

Codex Wiki

Mathematics

Area of mathematics

Algebra

Linear algebra

{c}
{title2=$AX-XB=C$}
{wiki}

The Sylvester equation $AX-XB=C$ has a unique solution $X$ for every $C$ exactly when $A$ and $B$ have disjoint spectra.


Sylvester equation

Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 2 / 10E / Solution

{wiki=Sylvester_equation}

The Sylvester equation is a type of linear matrix equation that has the general form: \\\[ AX + XB = C \\\] where: - \$A\$ and \$B\$ are given matrices of appropriate dimensions, - \$X\$ is the unknown matrix to be solved for, and - \$C\$ is a given matrix.


Sylvester equation ( $A X - XB = C$ )

 Ancestors (5)

 Incoming links (1)

 Discussion (0)

 Articles by others on the same topic (1)

Sylvester equation (AX−XB=C)

 Ancestors (5)

 Incoming links (1)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (1)

Sylvester equation ( $A X - XB = C$ )

 Discussion (0)