New bounds for the spread of a matrix using the radius of the smallest disc that contains all eigenvalues

Abstract

Let $\mathcal{D}$ denote the smallest disc  containing alleigenvalues of the matrix $A$. Without knowing the eigenvalues of$A$, we can estimate the spread of $A$ and the radius of$\mathcal{D}$. Some  new bounds for  the radius of $\mathcal{D}$ andthe spread of $A$ are given. These bounds involve the entries of$A$. Also sufficient conditions for  equality are obtained for someinequalities. New proofs of some known results are  presented too.