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An Identity of Hankel Matrices Generated from the Moments of Gaussian Distribution (2403.04052v1)
Published 6 Mar 2024 in cs.IT and math.IT
Abstract: In this letter, we proved a matrix identity of Hankel matrices that seems unrevealed before, generated from the moments of Gaussian distributions. In particular, we derived the Cholesky decompositions of the Hankel matrices in closed-forms, and showed some interesting connections between them. The results have potential applications in such as optimizing a nonlinear (NL) distortion function that maximizes the receiving gain in wireless communication systems.
- D. Macedo, J. Guerreiro, R. Dinis, and S. Hu, “On the design of nonlinear characteristics that optimize maximum likelihood OFDM performance,” IEEE Trans. Veh. Technol., vol. 72, no. 12, pp. 16882-16886, Dec. 2023.
- C. Hermite, “Sur un nouveau développement en série de fonctions,” C. R. Acad. Sci. Paris. 58: 93-100. Collected in Œuvres II, pp. 293-303, 1864.
- J. Phillips, “The triangular decomposition of Hankel matrices,” Mathematics of Computation, vo. 25, no. 115, pp. 599-602, Jul. 1971.
- D. L. Boley, F. T. Luk, and D. Vandevoorde, “A fast method to diagonalize a Hankel matrix,” Linear Algebra and its Applications, vol. 284, no. 1-3, pp. 41-52, Nov. 1988.
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