Araştırma Makalesi
Yıl 2025,
Cilt: 17 Sayı: 1, 26 - 32, 30.06.2025
Öz
This paper gives upper and lower bounds for the Frobenius norm of the commutator of the exchange matrix and the Cauchy-Hankel matrix of the form $H_n=\left(\dfrac{2}{1+2(i+j)}\right)_{i,j=1}^n$.
Anahtar Kelimeler
Kaynakça
- Audenaert, Koenraad M.R., Variance bounds, with an application to norm bounds for commutators, Linear Algebra and Its Applications, 432(2010), 1126–1143.
- Bozkurt, D., On ℓp norms of Cauchy-Toeplitz matrices, Linear and Multilinear Algebra, 44(1998), 341–346.
- Böttcher, A., Wenzel, D., How big can the commutator of two matrices be and how big is it typically?, Linear Algebra Appl., 403(2005), 216–228.
- Böttcher, A., Wenzel, D., The Frobenius norm and the commutator, Linear Algebra and Its Applications, 429(2008), 1864–1885.
- Chruscinski, D., Kimura, G., Ohno, H., Singal, T., One-parameter generalization of the B¨ottcher-Wenzel inequality and its application to open quantum dynamics, Linear Algebra and Its Applications, 656(2023), 158–166.
- Gil, M., A sharp bound for the Frobenius norm of self-commutators of matrices, Linear & Multilinear Algebra, 65(11)(2017), 2333–2339.
- Horn, R.A., & Johnson, C.R., Matrix Analysis, Cambridge University Press, 2012.
- Laszlo, L., Proof of B¨ottcher and Wenzel’s conjecture on commutator norms for 3-by-3 matrices, Linear Algebra Appl., 422(2007), 659–663.
- Lu, Z., Normal Scalar Curvature Conjecture and Its applications, Journal of Functional Analysis, 261(2011), 1284–1308.
- Moenck, R., On computing closed forms for summations, Proceedings of the MACSYMA User’s Conference, 225–236, 1977.
- Solak, S., Bahşi, M., On the Frobenius norm of commutator of Cauchy-Toeplitz matrix and exchange matrix, Turkish Journal of Mathematics, 47(5)(2023), 1550–1557.
- Solak, S., Bozkurt, D., On the spectral norms of Cauchy-Toeplitz and Cauchy-Hankel matrices, Applied Mathematics and Computations, 140(2003), 231–238.
- Solak, S., Bozkurt, D.,A note on bound for norms of Cauchy-Hankel matrices, Numerical Linear Algebra With Applications, 10(4)(2003), 377–382.
- Türkmen, R., Bozkurt, D., On the bounds for the norms of Cauchy-Toeplitz and Cauchy-Hankel matrices, Applied Mathematics and Computations, 132(2002), 633–642.
- Tyrtysnikov, E.E., Cauchy-Toeplitz matrices and some applications, Linear Algebra and its Applications, 149(1991), 1–18.
- Vong, S.W., Jin, X.Q., Proof of B¨ottcher and Wenzel’s conjecture, Oper. Matrices 2, (2008), 435–442.
- Wu, Y.D., Liu, X.Q., A short note on the Frobenius norm of the commutator, Mathematical Notes, 87(5/6)(2010), 903–907.
Yıl 2025,
Cilt: 17 Sayı: 1, 26 - 32, 30.06.2025
Öz
Kaynakça
- Audenaert, Koenraad M.R., Variance bounds, with an application to norm bounds for commutators, Linear Algebra and Its Applications, 432(2010), 1126–1143.
- Bozkurt, D., On ℓp norms of Cauchy-Toeplitz matrices, Linear and Multilinear Algebra, 44(1998), 341–346.
- Böttcher, A., Wenzel, D., How big can the commutator of two matrices be and how big is it typically?, Linear Algebra Appl., 403(2005), 216–228.
- Böttcher, A., Wenzel, D., The Frobenius norm and the commutator, Linear Algebra and Its Applications, 429(2008), 1864–1885.
- Chruscinski, D., Kimura, G., Ohno, H., Singal, T., One-parameter generalization of the B¨ottcher-Wenzel inequality and its application to open quantum dynamics, Linear Algebra and Its Applications, 656(2023), 158–166.
- Gil, M., A sharp bound for the Frobenius norm of self-commutators of matrices, Linear & Multilinear Algebra, 65(11)(2017), 2333–2339.
- Horn, R.A., & Johnson, C.R., Matrix Analysis, Cambridge University Press, 2012.
- Laszlo, L., Proof of B¨ottcher and Wenzel’s conjecture on commutator norms for 3-by-3 matrices, Linear Algebra Appl., 422(2007), 659–663.
- Lu, Z., Normal Scalar Curvature Conjecture and Its applications, Journal of Functional Analysis, 261(2011), 1284–1308.
- Moenck, R., On computing closed forms for summations, Proceedings of the MACSYMA User’s Conference, 225–236, 1977.
- Solak, S., Bahşi, M., On the Frobenius norm of commutator of Cauchy-Toeplitz matrix and exchange matrix, Turkish Journal of Mathematics, 47(5)(2023), 1550–1557.
- Solak, S., Bozkurt, D., On the spectral norms of Cauchy-Toeplitz and Cauchy-Hankel matrices, Applied Mathematics and Computations, 140(2003), 231–238.
- Solak, S., Bozkurt, D.,A note on bound for norms of Cauchy-Hankel matrices, Numerical Linear Algebra With Applications, 10(4)(2003), 377–382.
- Türkmen, R., Bozkurt, D., On the bounds for the norms of Cauchy-Toeplitz and Cauchy-Hankel matrices, Applied Mathematics and Computations, 132(2002), 633–642.
- Tyrtysnikov, E.E., Cauchy-Toeplitz matrices and some applications, Linear Algebra and its Applications, 149(1991), 1–18.
- Vong, S.W., Jin, X.Q., Proof of B¨ottcher and Wenzel’s conjecture, Oper. Matrices 2, (2008), 435–442.
- Wu, Y.D., Liu, X.Q., A short note on the Frobenius norm of the commutator, Mathematical Notes, 87(5/6)(2010), 903–907.
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2025 |
| Gönderilme Tarihi | 19 Eylül 2024 |
| Kabul Tarihi | 14 Mart 2025 |
| Yayımlandığı Sayı | Yıl 2025 Cilt: 17 Sayı: 1 |