Let A and B be square matrices over a field in which the minimum polynomial of A is completely reducible. It is shown that A is k commutative with respect to B for some non-negative integer k if and only if B commutes with every principal idempotent of A. The proof is brief, simplifying much of the previous study of k-commutative matrices. The result is also used to generalize some well-known theorems on finite matrix commutators that involve a complex matrix and its transposed complex conjugate.
Original Publication Citation
Robinson, D. W. "A Note on k-Commutative Matrices." Journal of Mathematical Physics 2 (1961): 776-777.
BYU ScholarsArchive Citation
Robinson, D. W., "A Note on k-Commutative Matrices" (1961). All Faculty Publications. 812.
Physical and Mathematical Sciences
Physics and Astronomy
© 1961 American Institue of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics and may be found at http://link.aip.org/link/?JMAPAQ/2/776/1
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