A link between the matrix equation AX –XB = C and the matrix quadratic
Abigail Ward · International Journal of Mathematical Education in Science and Technology · 1994
A link is established between Sylvester's linear matrix equation and the matrix quadratic equation whereby solutions of one can be deduced from those of the other. This (it is hoped) gives further insight into the structure of Sylvester's linear equation as well as achieving a method of obtaining some solutions of both matrix linear and quadratic equations.