New views of the doubly stochastic single eigenvalue problem

Charles Johnson, Stephen Newman, Ilya Spitkovsky

Research output: Contribution to journalArticlepeer-review


The question of which elements of the open unit disc occur as eigenvalues of n-by-n doubly stochastic matrices has long been open, in spite of a number of intriguing partial results. By enhancing a natural, but slightly false, conjecture, we gain some new computational insights into the problem. We also apply the classical field of values to give some partial results on both the necessity of certain component polygons of (Formula presented.) for other cycle lengths and the accuracy of the Perfect-Mirsky Conjecture in the neighborhoods of corners.

Original languageEnglish (US)
JournalLinear and Multilinear Algebra
StateAccepted/In press - 2022


  • 15A18
  • 15B51
  • boundary conjecture
  • convex combination
  • Doubly stochastic matrix
  • Perfect-Mirsky conjecture
  • permutation matrix

ASJC Scopus subject areas

  • Algebra and Number Theory


Dive into the research topics of 'New views of the doubly stochastic single eigenvalue problem'. Together they form a unique fingerprint.

Cite this