177
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Idempotence preserving maps between matrix spaces

, &
Pages 349-375 | Received 28 Oct 2010, Accepted 17 Jun 2011, Published online: 25 Aug 2011
 

Abstract

Suppose 𝔽 is an arbitrary field of characteristic not 2 and 𝔽 ≠ 𝔽3. Let M n (𝔽) be the space of all n × n full matrices over 𝔽 and P n (𝔽) the subset of M n (𝔽) consisting of all n × n idempotent matrices and GL n (𝔽) the subset of M n (𝔽) consisting of all n × n invertible matrices. Let Φ𝔽(n, m) denote the set of all maps from M n (𝔽) to M m (𝔽) satisfying A − λB ∈ P n (𝔽) ⇒ φ(A) − λφ(B) ∈ P m (𝔽) for every A, B ∈ M n (𝔽) and λ ∈ 𝔽, where m and n are integers with 3 ≤ n ≤ m. It is shown that if φ ∈ Φ𝔽(n, m), then there exists T ∈ GL m (𝔽) such that φ(A) = T [A ⊗ I p  ⊕ A t  ⊗ I q  ⊕ 0]T−1 for every A ∈ M n (𝔽), where I 0 = 0. This improves the results of some related references.

AMS Subject Classification:

Acknowledgements

This work is supported by the Postdoctoral Foundation of China (No. 520-415099) and the NSF of P.R. China (No.10871056). The authors would like to thank the referee for his valuable comments and suggestions to the earlier version of this article.

Log in via your institution

Log in to Taylor & Francis Online

PDF download + Online access

  • 48 hours access to article PDF & online version
  • Article PDF can be downloaded
  • Article PDF can be printed
USD 61.00 Add to cart

Issue Purchase

  • 30 days online access to complete issue
  • Article PDFs can be downloaded
  • Article PDFs can be printed
USD 670.00 Add to cart

* Local tax will be added as applicable

Related Research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.