On the matrix equation XA + AX^T = 0

2012/08/02 by Stephan Ramon Garcia, Garcia, Stephan Ramon, Amy L. Shoemaker +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1208.1238

Abstract

The matrix equation XA + AX^T = 0, which has relevance to the study of Lie algebras, was recently studied by De Teran and Dopico. They reduced the study of this equation to several special cases and produced explicit solutions in most instances. In this note we obtain an explicit solution in one of the difficult cases, for which only the dimension of the solution space and an algorithm to find a basis of this space were known previously.

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