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<p>In this paper, we explored a degenerate form of the Hermite matrix, defined using <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( \lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>-rising sequences, and investigated its various properties. We obtained the matrix’s powers, inverses, and different factorizations. Additionally, we derived results concerning its eigenvalues and eigenvectors. Furthermore, we expressed it in exponential form by relating it to special matrices.</p>

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Various factorizations and applications of the degenerate hermite matrix

  • 期刊论文

  • 发表日期：

    2025年12月6日

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  • Gonca Kizilaslan,
  • Taekyun Kim

摘要

In this paper, we explored a degenerate form of the Hermite matrix, defined using \( \lambda \) λ -rising sequences, and investigated its various properties. We obtained the matrix’s powers, inverses, and different factorizations. Additionally, we derived results concerning its eigenvalues and eigenvectors. Furthermore, we expressed it in exponential form by relating it to special matrices.