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)
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