Explore: Sylvester Equations

In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of the form: A X + X B = C . {\displaystyle AX+XB=C.} It is

one. Sylvester cyclotomic numbers. The Sylvester equation, AX + XB = C where A, B, C are given matrices and X is an unknown matrix. Sylvester's "four

and B {\displaystyle B} are stable, then the unique solution to the Sylvester equation, A X + X B = C {\displaystyle AX+XB=C} , is given by X {\displaystyle

the continuous time and discrete time Lyapunov equations can be expressed as solutions of a matrix equation. Furthermore, if the matrix A {\displaystyle

Hessenberg–Schur algorithm. It remains a standard approach for solving Sylvester equations when X {\displaystyle X} is of small to moderate size. Let X , C

exists. The name Riccati is given to these equations because of their relation to the Riccati differential equation. Indeed, the CARE is verified by the time

series, 2 : 391–410; Sylvester coined the term "discriminant" on page 406. J. J. Sylvester (1879) "On certain ternary cubic-form equations," American Journal

and the Kronecker product. They arise in solving matrix equations such as the Sylvester equation. There are three types of row operations: row addition

This is a list of scientific equations named after people (eponymous equations). Contents A B C D E F G H I J K L M N O P R S T V W Y Z See also References

iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and