Realizing Suleimanova Spectra via Permutative Matrices

Abstract

A permutative matrix is a square matrix such that every row is a permutation of the first row. A constructive version of a result attributed to Suleimanova is given via permutative matrices. In addition, we strengthen a well-known result by showing that all realizable spectra containing at most four elements can be realized by a permutative matrix or by a direct sum of permutative matrices. We conclude by posing a problem.

Cited by in corpus (3)

• Row Cones, Perron Similarities, and Nonnegative Spectra
• Inverse problems for symmetric doubly stochastic matrices whose Suleĭmanova spectra are bounded below by 1/2
• A characterization of orthogonal permutative matrices of order 4