Student Co-author

Pomona Undergraduate

Document Type

Article - preprint


Mathematics (Pomona)

Publication Date



Congruence, Congruence canonical form, Lie algebra, Pascal’s triangle, Pascal matrix


The matrix equation XA+AXT=0, which has relevance to the study of Lie algebras, was recently studied by De Terán and Dopico (Linear Algebra Appl. 434 (2011), 44–67). 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


Pre-print from

Final publication can be found at:

Stephan Ramon Garcia, Amy L. Shoemaker, On the matrix equation, Linear Algebra and its Applications, Volume 438, Issue 6, 15 March 2013, Pages 2740-2746, ISSN 0024-3795, (

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© 2013 Elsevier B.V.

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