DECOMPOSING MATRICES ON AN INFINITE FIELD INTO COMMUTATORS OF UNIPOTENT MATRICES OF INDEX 2
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Abstract
Let be a field and a matrix in the special linear group over . Hou (2021) has shown that if is the field of complex numbers, can be decomposed into a product of two commutators of unipotent matrices of index . In this paper, we will extend the above result for the case when is an infinite field. Particularly, we will prove that every nonscalar matrix over an infinite field can be decomposed into a product of at most two commutators of unipotent matrices of index .
Keywords
commutator, infinite field, nonscalar matrix, special linear group, unipotent matrices of index
Article Details
References
Hou, X. (2021). Decomposition of matrices into commutators of unipotent matrices of index 2. The Electronic Journal of Linear Algebra, 37, 31-34.
Sourour, A. R. (1986). A factorization theorem for matrices. Linear and Multilinear Algebra, 19(2), 141-147.
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,
123-130.
Wang, J. H., & Wu, P. Y. (1991). Products of unipotent matrices of index 2. Linear Algebra and its Applications, 149, 111-123.
Zheng, B. (2002). Decomposition of matrices into commutators of involutions. Linear algebra and its applications, 347(1-3), 1-7.