#### 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). *All Faculty Publications*. 812.

http://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/