Keywords
matrices, k-commutative
Abstract
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). Faculty Publications. 812.
https://scholarsarchive.byu.edu/facpub/812
Document Type
Peer-Reviewed Article
Publication Date
1961-11-01
Permanent URL
http://hdl.lib.byu.edu/1877/1239
Publisher
AIP
Language
English
College
Physical and Mathematical Sciences
Department
Physics and Astronomy
Copyright Status
© 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
Copyright Use Information
http://lib.byu.edu/about/copyright/