Upper bounds for the spread of a matrix
Suppose \(A\) is an \(n\times n\) complex matrix with eigenvalues \(\lambda_1,\ldots,\lambda_n\). The spread of \(A\), denoted by \(s(A)\), is defined by \(s(A)=\max_{i,j}|\lambda_i-\lambda_j|\). The authors provide new and sharper upper bounds of \(s(A)\), refining some bounds due to \textit{L. Mirsky} [Mathematika, Lond. 3, 127--130 (1956; Zbl 0073.00903)] and \textit{Y. Gu} [Acta Math. Appl. Sin. 17, No. 4, 501--511 (1994)].
scientific article; zbMATH DE number 6104576