2015/05/13 by Vladimir Bolotnikov, Bolotnikov, Vladimir
Mathematics · Computer Science · #Algebraic and Geometric Analysis #Matrix Theory and Algorithms #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1505.03575
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)