Unipotency of Matrix Group Generated by Two Matrices

In this paper, the problem of unipotency for the matrix group generated by two matrices is examined. By employing matrix logarithms as a tool, various combinatorial formulas for matrices were derived by selecting different primitive elements. Key conclusions were then reached through the organizatio...

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Bibliographic Details
Published inJournal of applied mathematics Vol. 2025; no. 1
Main Authors Cheng, Yanshuo, Yang, Xinsong
Format Journal Article
LanguageEnglish
Published New York John Wiley & Sons, Inc 01.01.2025
Wiley
Subjects
Investigations
Jordan
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ISSN1110-757X
1687-0042
DOI10.1155/2025/1423635

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Summary:In this paper, the problem of unipotency for the matrix group generated by two matrices is examined. By employing matrix logarithms as a tool, various combinatorial formulas for matrices were derived by selecting different primitive elements. Key conclusions were then reached through the organization and simplification of these formulas. It was ultimately demonstrated, based on these conclusions, that a matrix group G generated by two matrices, where the Jordan blocks do not exceed third order, must be unipotent if each primitive element of G is unipotent and has an order of six or less.
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ISSN:1110-757X
1687-0042
DOI:10.1155/2025/1423635