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Dergiler / Gazi University Journal of Science / 2026 / Volume: 39 Issue: 1

On The Frobenius Norm of Commutators Involving Exponential Matrices

Ahmet Öksüz(NECMETTİN ERBAKAN ÜNİVERSİTESİ)0000-0002-7355-5176
Süleyman Solak(NECMETTIN ERBAKAN UNIVERSITY)0000-0003-4085-277X
Sayfa
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Yayın Tarihi
2026-01-10
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we obtain upper bounds for the Frobenius norms of these commutators.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we first establish a different generalization of the equality proposed by Farhadian for iterated exponentials with the matrix J_n, where J_n is an n×n matrix with all entries equal to 1.
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Temel Bulgular & Veri:Then, using this new generalization, we derive commutator identities involving iterated exponential matrices.
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Sonuç & Katkı:Finally, we obtain upper bounds for the Frobenius norms of these commutators.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Matrix commutators · Matrix exponential · Frobenius norm

Abstract

In this paper, we first establish a different generalization of the equality proposed by Farhadian for iterated exponentials with the matrix J_n, where J_n is an n×n matrix with all entries equal to 1. Then, using this new generalization, we derive commutator identities involving iterated exponential matrices. Finally, we obtain upper bounds for the Frobenius norms of these commutators.

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Bu Makaleye Atıf Yap

Öksüz, A., Solak, S. (2026). On The Frobenius Norm of Commutators Involving Exponential Matrices. Gazi University Journal of Science, Volume: 39 Issue: 1. https://doi.org/10.35378/gujs.1712615

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Kaynakça (14)

  1. Farhadian, R., “A note on the exponential of a matrix whose elements are all 1”, Applied Mathematics e-Notes, 18: 92-99, (2018).
  2. Audenaert, KMR., “Variance bounds, with an application to norm bounds for commutators”, Linear Algebra and Its Applications, 432: 1126-1143, (2010). DOI: http://dx.doi.org/10.1016/j.laa.2009.10.022
  3. Chruściński, D., Kimura G., Ohno H. and Singal, T., “One-parameter generalization of the Böttcher-Wenzel inequality and its application to open quantum dynamics”, Linear Algebra and Its Applications, 656: 158–166, (2023). DOI: https://doi.org/10.1016/j.laa.2022.09.022
  4. Böttcher, A., Wenzel, D., “How big can the commutator of two matrices be and how big is it typically?”, Linear Algebra and Its Applications, 403: 216–228, (2005). DOI: http://dx.doi.org/10.1016/j.laa.2005.02.012
  5. Böttcher, A., Wenzel, D., “The Frobenius norm and the commutator”, Linear Algebra and Its Applications, 429: 1864-1885, (2008). DOI: http://dx.doi.org/10.1016/j.laa.2008.05.020
  6. Wu, Y.-D., Liu, X-Q., “A short note on the Frobenius norm of the commutator”, Mathematical Notes, 87(5/6): 903-907, (2010). DOI: https://doi.org/10.1134/s0001434610050305
  7. Solak, S., Bahşi̇, M., “On the Frobenius norm of commutator of Cauchy-Toeplitz matrix and exchange matrix”, Turkish Journal of Mathematics, 47(5): 1550–1557, (2023). DOI: https://doi.org/10.55730/1300-0098.3447
  8. Gil’, M., “A sharp bound for the Frobenius norm of self-commutators of matrices”, Linear & Multilinear Algebra, 65(11), 2333–2339, (2017). DOI: https://doi.org/10.1080/03081087.2016.1273875
  9. Smith, J.M., "A Theorem on Matrix Commutators", Journal of Research of the Notional Bureau of Standard- B. Mathematical Sciences, 758: 17-21, (1971).
  10. Kan, O., Solak, S., “Commutators Involving Matrix Functions”, Electronic Journal of Linear Algebra, 33: 113-121, (2018). DOI: https://doi.org/10.13001/1081-3810.3684
  11. Bellman, R., “Introduction to Matrix Analysis” 2nd ed., Philadelphia, (1997).
  12. Horn, R.A., Johnson, C.R., “Matrix Analysis”, Cambridge University Press, (2012).
  13. Hall, B. C., “Lie Groups, Lie Algebras, and Representations- An Elementary Introduction” 2nd ed., Springer, Switzerland, (2015).
  14. Bernstein, D.S., “Matrix Mathematics- Theory, Facts, and Formulas”, New Jersey, (2009).