On the Crossing Rule.

Abstract

The paper gives conditions on a family of matrices which guarantee that some matrix in the family will have a multiple eigenvalue. In particular, the main theorem states exactly which dimensions admit k dimensional subspaces of matrices for which all nonzero elements have distinct eigenvalues. This question arises naturally in the theory of first order hyperbolic systems of partial differential equations; the main theorem, in this context, tells exactly for which integers n an n x n system in k space variables may be strictly hyperbolic. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1982
Accession Number
ADA120957

Entities

People

  • J. H. Sylvester
  • J. W. Robbin
  • S. Friedland

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algebra
  • Algebraic Topology
  • Cauchy Problem
  • Classification
  • Contracts
  • Differential Equations
  • Eigenvalues
  • Equations
  • Geometric Forms
  • Geometry
  • Materials
  • Mathematics
  • Partial Differential Equations
  • United States
  • Universities
  • Vector Spaces
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Educational Psychology
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research

Technology Areas

  • Space