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<p>We establish a special triangular form of polynomial 3 × 3-matrices of simple structure relative to the semiscalar equivalence. We propose a method for the construction of matrices of this form. The invariants are found for matrices of this form and the conditions for their semiscalar equivalence are established. The method for the construction of transforming matrices under the transition from one matrix of a special triangular form to another is proposed.</p>

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On the Triangular Form of 3 × 3-Matrices of Simple Structure Relative to Semiscalar Equivalence

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • B. Z. Shavarovskii

摘要

We establish a special triangular form of polynomial 3 × 3-matrices of simple structure relative to the semiscalar equivalence. We propose a method for the construction of matrices of this form. The invariants are found for matrices of this form and the conditions for their semiscalar equivalence are established. The method for the construction of transforming matrices under the transition from one matrix of a special triangular form to another is proposed.