A NOTE ON DECOMPOSITIONS OF MATRICES IN THE CENTRALIZER OF A WEYR MATRIX
Main Article Content
Abstract
Let be an algebraically closed field of characteristic not equal to , and be a positive integer. Assume is a basic Weyr matrix with a homogeneous Weyr structure of length and denotes the centralizer of in . This paper describes the subgroup generated by commutators of involutions in . Furthermore, we show that every matrix in this subgroup can be expressed as a product of at most commutators of involutions in .
Keywords
commutator, involution, matrix centralizer, matrix decomposition, Weyr matrix
Article Details
References
Djoković, D. Ž. (1967). Product of two involutions. Archiv der Mathematik, 18, 582–584.
Hou, X. (2019). Decomposition of infinite matrices into products of commutators of involutions. Linear Algebra and its Applications, 563, 231–239. https://doi.org/10.13001/ela.2022.7091
O'Meara, K. C., Clark, J., & Vinsonhaler, C. I. (2011). Advanced Topics in Linear Algebra.
Oxford University Press.
Tran, N. S., Truong, H. D., Nguyen, T. T. H, & Mai, H. B. (2022). On decompositions of matrices into products of commutators of involutions. The Electronic Journal of Linear Algebra, 38, 123–130. https://doi.org/10.13001/ela.2022.6797
Wonnenburger, M. J. (1966). Transformations which are products of two involutions. Journal of Mathematics and Mechanics, 16(4), 327–338.
Zheng, B. (2002). Decomposition of matrices into commutators of involutions. Linear Algebra and its Applications, 347, 1–7.