Characteristic Roots, Eigenvalues and Eigenvectors of a Certain Type of 4×4 Dual Tridiagonal Matrices

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Dursun P., Gürses N.

TURAN-Fundamental Sciences Symposium (TURAN25), İstanbul, Turkey, 23 - 26 June 2025, pp.36, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.36
  • İstanbul Ticaret University Affiliated: Yes

Abstract

Dual number matrices serve as effective tools in modeling problems in brain science and multi-agent formation control. In the literature one can find determinants, characteristic polynomials, eigenvalues, and eigenvectors of dual number matrices. An n x n  dual number matrix may have exactly n eigenvalues, none, or infinitely many. In this presentation, by taking a certain type of  4 x 4 dual number tridiagonal matrix,  we demonstrate that it has exactly four eigenvalues, which directly result from structured combinations of the eigenvalues of its real matrix components. Finally, we present illustrative examples that support and clarify our theoretical findings.

Keywords: Dual numbers, Characteristic polynomial, Eigenvalues, Tridiagonal matrix,

 

References

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