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<p>Frank matrices are notable in matrix analysis for their characteristic structural and spectral properties. Motivated by the tools of <i>q</i>-calculus, we define a <i>q</i>-analogue of the Frank matrix and study its algebraic properties, such as the determinant, inverse, <i>LU</i> decomposition, characteristic polynomial, eigenvalues (with the help of Sturm’s Theorem), and certain norms. This extension generalizes the Frank matrix and provides new insights into its structural and spectral behaviour.</p>

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The q-analogue of the Frank matrix

  • 期刊论文

  • 发表日期：

    2025年12月18日

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  • Efruz Özlem Mersin

摘要

Frank matrices are notable in matrix analysis for their characteristic structural and spectral properties. Motivated by the tools of q-calculus, we define a q-analogue of the Frank matrix and study its algebraic properties, such as the determinant, inverse, LU decomposition, characteristic polynomial, eigenvalues (with the help of Sturm’s Theorem), and certain norms. This extension generalizes the Frank matrix and provides new insights into its structural and spectral behaviour.