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Conditions of Semiscalar Equivalence of One Class 3×3 Matrices of Simple Structure

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  • B. Z. Shavarovskii

Abstract

This paper solves the problem of classifying matrices over a ring of polynomials up to semiscalarly equivalence transformations. For the selected set of polynomial matrices of simple structure, the so‐called oriented by characteristic roots reduced matrix is constructed. The latter, in addition to the triangular form and the presence of invariant factors on the main diagonal, has some predefined properties. Invariants and conditions of semiscalar equivalence are established for such matrices.

Suggested Citation

  • B. Z. Shavarovskii, 2022. "Conditions of Semiscalar Equivalence of One Class 3×3 Matrices of Simple Structure," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:8395922
    DOI: 10.1155/2022/8395922
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    1. B. Z. Shavarovskii & Shaofang Hong, 2021. "Oriented by Characteristic Roots Reduced Matrices in the Class of Semiscalarly Equivalent," Journal of Mathematics, Hindawi, vol. 2021, pages 1-6, April.
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