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Linear Relations Between Higher Matrix Commutators

Published online by Cambridge University Press:  20 November 2018

Nisar A. Khan
Nisar A. Khan*
Affiliation:
Muslim University, Aligarh, India
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Let Mn denote the space of all n-square matrices over an algebraically closed field F. For A, B ∊ Mn, let

define the iterated commutators of A and B. Recently several research papers (1, 2, 4, and 5) have appeared on these commutators. In (1), Kato and Taussky have proved that for n = 2 the iterated commutators of A and B satisfy the linear relation

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 315 - 320
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Kato, T. and Taussky, O., Commutators of A and A*, J. Washington Acad. Sci., 4-6 (1956), 38–40.Google Scholar
2. Marcus, M. and Khan, N. A., On matrix commutators, Can. J. Math., 12 (1960), 269–277.Google Scholar
3. Perlis, S., Theory of matrices (New York, 1952).Google Scholar
4. Smiley, M. F., Matrix commutators, Can. J. Math., 13 (1961), 353–355.Google Scholar
5. Taussky, O. and Wielandt, H., Linear relations between higher additive commutators, Proc. Am. Math. Soc, 13 (1962), 732–735.Google Scholar