On the euclidean and the spectral norms of quaternion Cauchy-Toeplitz and quaternion Cauchy-Hankel matrices

Abstract

In this study, we have established upper and lower bounds for the Euclidean and the Spectral norms of Quaternion Cauchy-Toeplitz ( T ) and Quaternion Cauchy-Hankel ( H ) matrices respectively. Besides, by assuming complex matrix T A A j n  1  2 , we have defined the matrix         2 1 1 2 [ ] A A A A Tn and similarly, by assuming complex matrix H B B j n  1  2 , we have also defined another matrix         2 1 1 2 [ ] B B B B Hn . Then we have obtained the bounds of the spectral norms for these matrices.

Bu çalışmada, sırasıyla Quaternion Cauchy-Toeplitz ( T ), Quaternion Cauchy-Hankel ( H ) Matrislerinin Spektral ve Euclidean normlar için alt ve üst sınarlar elde ettik. Ayrıca, T A A j n  1  2 , kompleks matrisi yardımıyla         2 1 1 2 [ ] A A A A Tn matrisini ve benzer şekilde H B B j n  1  2 , kompleks matrisi yardımıyla         2 1 1 2 [ ] B B B B Hn matrisini tanımlayıp bu matrislerin spektral normlar için sınırlar elde ettik.