On the Lower and Upper Bounds for the Euclidean Norm of a Complex Matrix and Its Applications

Abstract

In this study, we obtained lower and upper bounds for the Euclidean norm of a complex matrix $A$ of order $n\times n$. In addition,
we found lower and upper bounds for the spectral norms and Euclidean norms of the Hilbert matrix its Hadamard
square root, Cauchy-Toeplitz and Cauchy-Hankel matrices in the forms $H={\left(\frac{1}{i+j–1}\right)}_{i,j=1}^n$,$H^{\frac{01}{2}}=({\frac{1}{(i+j-1)}}^{\frac{1}{2}}{)}_{i,j=1}^n$; $T_n=\left[{\frac{1}{(g+(i+j)h)}}_{i,j=1}^n\right]$, and $H_n={\left[\frac{1}{(g+(i+j)h}\right]}_{i,j=1}^n$, respectively.