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

Dursun P., Gürses N.

TURAN-Fundamental Sciences Symposium (TURAN25), İstanbul, Türkiye, 23 - 26 Haziran 2025, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

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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