On the Sylvester Equation over Quaternions
The Sylvester equation \(AX\;-\;XB\;=\;C\) is considered in the setting of quaternion matrices. Conditions that are necessary and sufficient for the existence of a unique solution are well known. We study the complementary case where the equation either has infinitely many solutions or does not have solutions at all. Special attention is given to the case where A and B are, respectively, lower and upper triangular two-diagonal matrices (in particular, if A and B are Jordan blocks).
KeywordsSylvester equation polynomial interpolation
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