Many applications, in particular the stability analysis of differential equations, lead to linear matrix equations, such as \(AX+XB=C\). Here the matrices A, B, C are given and the goal is to determine a matrix X that solves the equation (we will give a formal definition below). In the description of the solutions of such equations, the Kronecker product another product of matrices, is useful. In this chapter we develop the most important properties of this products and we study its application in the context of linear matrix equations.
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