Multiplicative principal-minor inequalities for totally nonnegative matrices

  • Authors:

  • Shaun M Fallat;Michael I Gekhtman;Charles R Johnson

  • Affiliations:

  • Department of Mathematics and Statistics, University of Regina, Regina, SK S4S 0A2, Canada;Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556-5683, USA;Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA

  • Venue:
  • Advances in Applied Mathematics
  • Year:
  • 2003

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Abstract

An m-by-n matrix A is said to be totally nonnegative if every minor of A is nonnegative. Our main interest lies in characterizing all the inequalities that exist among products of principal minors of totally nonnegative matrices. We provide a complete description of all such inequalities for n-by-n totally nonnegative matrices with n=