Authors

D. W. Robinson

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.

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

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