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Many applications, in particular the stability analysis of differential equations, lead to linear matrix equations, such as the Sylvester equation \(AX+XB=C\) . Here the matrices \(A,B,C\) are given and the goal is to determine a matrix X that solves the equation. 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 product and we study its application in the context of linear matrix equations.

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The Kronecker Product and Linear Matrix Equations

  • 章节

  • 发表日期：

    2025年

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  • Jörg Liesen,
  • Volker Mehrmann

摘要

Many applications, in particular the stability analysis of differential equations, lead to linear matrix equations, such as the Sylvester equation \(AX+XB=C\) . Here the matrices \(A,B,C\) are given and the goal is to determine a matrix X that solves the equation. 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 product and we study its application in the context of linear matrix equations.