✦ LIBER ✦

How to solve the matrix equation

✍ Scribed by Gerald Bourgeois

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 217 KB
Volume: 434
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.09.037

No coin nor oath required. For personal study only.

✦ Synopsis

Let f be an analytic function defined on a complex domain and A ∈ M n (C). We assume that there exists a unique α satisfying f (α) = 0. When f (α) = 0 and A is non-derogatory, we completely solve the equation XA -AX = f (X). This generalizes Burde's results. When f (α) / = 0, we give a method to solve com- pletely the equation XA -AX = f (X): we reduce the problem to solving a sequence of Sylvester equations. Solutions of the equation f (XA -AX) = X are also given in particular cases.

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