Rank, trace, eigenvalues and norms of a structured matrix

Abstract

The paper deals with rank, trace, eigenvalues and norms of the matrix [Formula: see text], where [Formula: see text] are ith components of any real sequence [Formula: see text]. A result in this paper is that the Euclidean and spectral norms of the matrix [Formula: see text] is [Formula: see text]. This is a generalization of the main result by Solak [Appl. Math. Comput. 232 (2014) 919–921], with the proof based on a simple property of norms of real matrices.