On explicit formulas of hyperbolic tangent matrix function

Laarichi, Yassine; Ftouhi, Mostafa; Gretete, Driss

doi:10.47974/JIM-1798

Open Access Research Article

On explicit formulas of hyperbolic tangent matrix function

^*Yassine LaarichiCorresponding authoryassine.Laarichi@uit.ac.maDepartment of MathematicsUniversity Ibn TofailKenitra, MoroccoView full profile → , Mostafa FtouhiDepartment of MathematicsUniversity Ibn TofailKenitra, MoroccoView full profile → , Driss Gretetedriss.gretete@uit.ac.maEngineering Sciences LaboratoryNational School of Applied SciencesIbn Tofail UniversityKenitra, MoroccoView full profile →

* Corresponding author · click or hover a name for details

pp. 1371–1381Vol. 27Issue 6September 2024DOI: 10.47974/JIM-1798XML

Received:: 01 Jul 2023
Published Online:: 30 Sep 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1798
Pages:: 1371–1381

Abstract

The hyperbolic tangent matrix function is a mathematical tool with diverse applications in various fields of mathematics, applied science, and engineering. The hyperbolic tangent matrix th(M), (M ∈ Mr (C)) can be determined through different techniques. In this paper, we establish several explicit formulas for th(tM). The first approach is based on Hermite matrix polynomial expansions, the second utilizes the decomposition of Fibonacci-Hörner, and the third involves polynomial decomposition utilizing the expression for the n-th power of the matrix and the polynomial decomposition of the exponential matrix. An example is provided to illustrate these methods.

Keywords

Matrix functions Hyperbolic tangent matrix function Explicit formulas Hermite matrix polynomials Fibonacci-horner decomposition

Subject Classifications

(2010) 11B3965F6026D0533B10

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