On the Sylvester Equation over Quaternions

  • Vladimir BolotnikovEmail author
Part of the Operator Theory: Advances and Applications book series (OT, volume 252)


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).


Sylvester equation polynomial interpolation 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsThe College of William and MaryWilliamsburgUSA

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