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Similarity Classes of Linear Transformations


Affiliations
1 Department of Mathematics, Central University of Jharkhand, Ranchi, India
     

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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.

Keywords

Vector Spaces, Linear transformations, Finitely generated modules, Partitions of integers
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  • Similarity Classes of Linear Transformations

Abstract Views: 82  |  PDF Views: 0

Authors

Puja Bharti
Department of Mathematics, Central University of Jharkhand, Ranchi, India
Jagmohan Tanti
Department of Mathematics, Central University of Jharkhand, Ranchi, India

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.

Keywords


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

References





DOI: https://doi.org/10.18311/jims%2F2020%2F25448