The altered Hermite matrix: implications and ramifications

Gonca Kizilaslan; Gonca Kizilaslan

doi:10.3934/math.20241238

AIMS Mathematics

2024, Volume 9, Issue 9: 25360-25375. doi: 10.3934/math.20241238

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Research article

The altered Hermite matrix: implications and ramifications

Gonca Kizilaslan ^,

Department of Mathematics, Faculty of Engineering and Natural Sciences, Kırıkkale University, TR-71450 Kırıkkale, Turkey

Received: 27 June 2024 Revised: 13 August 2024 Accepted: 19 August 2024 Published: 30 August 2024
MSC : 11C08, 05A10, 11B83, 15A23, 15B05

Matrix theory is essential for addressing practical problems and executing computational tasks. Matrices related to Hermite polynomials are essential due to their applications in quantum mechanics, numerical analysis, probability, and signal processing. Their orthogonality, recurrence relations, and spectral properties make them a valuable tool for both theoretical research and practical applications. From a different perspective, we introduced a variant of the Hermite matrix that incorporates triple factorials and demonstrated that this matrix satisfies various properties. By utilizing effective matrix algebra techniques, various algebraic properties of this matrix have been determined, including the product formula, inverse matrix and eigenvalues. Additionally, we extended this matrix to a more generalized form and derived several identities.
- Pascal-like matrix,
- Hermite polynomials,
- degenerate Hermite polynomials,
- factorization of matrix,
- Toeplitz matrix
Citation: Gonca Kizilaslan. The altered Hermite matrix: implications and ramifications[J]. AIMS Mathematics, 2024, 9(9): 25360-25375. doi: 10.3934/math.20241238

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Abstract

Matrix theory is essential for addressing practical problems and executing computational tasks. Matrices related to Hermite polynomials are essential due to their applications in quantum mechanics, numerical analysis, probability, and signal processing. Their orthogonality, recurrence relations, and spectral properties make them a valuable tool for both theoretical research and practical applications. From a different perspective, we introduced a variant of the Hermite matrix that incorporates triple factorials and demonstrated that this matrix satisfies various properties. By utilizing effective matrix algebra techniques, various algebraic properties of this matrix have been determined, including the product formula, inverse matrix and eigenvalues. Additionally, we extended this matrix to a more generalized form and derived several identities.

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