Similarity Classes of Linear Transformations

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Authors

  • Department of Mathematics, Central University of Jharkhand, Ranchi ,IN
  • Department of Mathematics, Central University of Jharkhand, Ranchi ,IN

DOI:

https://doi.org/10.18311/jims/2020/25448

Keywords:

Vector Spaces, Linear transformations, Finitely generated modules, Partitions of integers

Abstract

In this paper, we investigate the similarity classes of linear transformations on a vector space using structure theorem for finitely generated modules over a principal ideal domain. We also establish formulae to count similarity classes with a given polynomial as a characteristic polynomial and to count total number of classes when the scalar field is finite.

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Published

2020-07-01

How to Cite

Bharti, P., & Tanti, J. (2020). Similarity Classes of Linear Transformations. The Journal of the Indian Mathematical Society, 87(3-4), 148–164. https://doi.org/10.18311/jims/2020/25448
Received 2020-06-07
Accepted 2023-01-30
Published 2020-07-01

 

References

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K. Hoffman and R. Kunze, Linear Algebra, Second Edition, Prentice-Hall, New Delhi, 1991.

K. E. Morrison, Integer sequences and matrices over finite fields, J. Integer Sequences, 9. (6.2.1)(2006), 1–27.