On the Matrix Equation XA + AX_T = 0

Authors

Stephan Ramon Garcia, Pomona CollegeFollow
Amy L. Shoemaker '14, Pomona College

Student Co-author

Pomona Undergraduate

Document Type

Article - preprint

Department

Mathematics (Pomona)

Publication Date

2012

Keywords

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

Abstract

The matrix equation XA+AX^T=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

Comments

Pre-print from http://arxiv.org/abs/1208.1238

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, http://dx.doi.org/10.1016/j.laa.2012.10.041. (http://www.sciencedirect.com/science/article/pii/S0024379512007719)

Rights Information

© 2013 Elsevier B.V.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1016/j.laa.2012.10.041

Recommended Citation

Garcia, Stephan Ramon and Shoemaker, Amy L. '14, "On the Matrix Equation XA + AX_T = 0" (2012). Pomona Faculty Publications and Research. 243.
https://scholarship.claremont.edu/pomona_fac_pub/243