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<p>Matrix theory holds significant importance for the resolution of certain real-world problems and computational processes. Specific types of matrices and their linear algebraic properties are of considerable significance. In this paper, we analyse the main features of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2530_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation>-min and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2530_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation>-max matrices with harmonic higher order Gauss Fibonacci numbers entries, namely the inverse, determinant, permanent, and norms. Several recurrence relations for the characteristic polynomials will be also established. To verify our results, we present, as a pertinent application, the aforementioned properties of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2530_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation>-min matrix, whose entries are harmonic higher order Gauss Fibonacci numbers.</p>

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r-min and r-max matrices with harmonic higher order Gauss Fibonacci numbers entries

  • 期刊论文

  • 发表日期：

    2025年7月4日

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  • Milica Anđelić,
  • Carlos M. Da Fonseca,
  • Can Kızılateş,
  • Nazlıhan Terzioğlu

摘要

Matrix theory holds significant importance for the resolution of certain real-world problems and computational processes. Specific types of matrices and their linear algebraic properties are of considerable significance. In this paper, we analyse the main features of the \(r\) -min and \(r\) -max matrices with harmonic higher order Gauss Fibonacci numbers entries, namely the inverse, determinant, permanent, and norms. Several recurrence relations for the characteristic polynomials will be also established. To verify our results, we present, as a pertinent application, the aforementioned properties of the \(r\) -min matrix, whose entries are harmonic higher order Gauss Fibonacci numbers.