# THE MATRIX EQUATION XA −AX = f(X)

@inproceedings{Bourgeois2010THEME, title={THE MATRIX EQUATION XA −AX = f(X)}, author={G. Bourgeois}, year={2010} }

Let f be an analytic function defined on a complex domain and A 2 M n(C). We assume that there exists a uniquesatisfying f(�) = 0. When f 0 (�) = 0 and A is non derogatory, we solve completely the equation XA−AX = f(X). This generalizes Burde's results. When f 0 (�) 6 0, we give a method to completely solve the equation XA − AX = f(X). Solutions of the equation f(XA − AX) = X are also given in particular cases.

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