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A remark on oscillatory matrices

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
393
Identifiers
DOI: 10.1016/j.laa.2003.12.006
Keywords
  • Oscillatory Matrices
  • Planar Diagrams
  • Totally Nonnegative Matrices
  • Bidiagonal Factorizations

Abstract

Abstract In this note we revisit a classical criterion obtained by Gantmacher and Krein for determining when a totally nonnegative matrix is actually oscillatory. A new proof of this criterion is presented by incorporating bidiagonal factorizations of invertible totally nonnegative matrices and utilizing certain associated weighted planar diagrams.

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