Diagonal entries of inverses of diagonally dominant matrices

C. R. Johnson, C. Marijuán, M. Pisonero, I. M. Spitkovsky

Research output: Contribution to journalArticlepeer-review


We consider invertible, row diagonally dominant real matrices and give inequalities on their minors and diagonal entries of their inverses. A very special case is that all diagonal entries of an inverse, of a row stochastic, row diagonally dominant and invertible matrix, are at least 1, with strict inequality at least when the dominance is strict. This was conjectured in international trade theory in economics and motivated the present work (though much more is proven). Some of the results generalize previously known facts for M-matrices.

Original languageEnglish (US)
Pages (from-to)84-90
Number of pages7
JournalLinear Algebra and Its Applications
StatePublished - Jul 1 2024


  • Diagonal dominance of the column entries
  • Diagonal entries of the inverse
  • Diagonally dominant matrices
  • Inequalities for minors
  • Stochastic matrices

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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