On a generalized Jordan form of an infinite upper triangular matrix

Abstract

Any square matrix over an algebraically closed field has a Jordan normal form. In this paper, we prove that every infinite upper triangular matrix over an arbitrary field has a generalized infinite Jordan normal form.

Keywords:

• Infinite-dimensional vector space
• Jordan cannonical form
• matrix ring

AMS CLASSIFICATIONS:

• 15A03
• 15A21
• 15A99

Acknowledgements

The authors would like to thank the anonymous referee for the careful reading of this manuscript and very useful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

First, second and fourth authors are partially supported by Ministry of Education, Science and Technological Development of Republic of Serbia (Ministarstvo Prosvete, Nauke i Tehnološkog Razvoja) Project #174032.