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Simple waves do not avoid eigenvalue crossings
Author(s) -
Chumakova Lyuba,
Tabak Esteban G.
Publication year - 2010
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20288
Subject(s) - eigenvalues and eigenvectors , simple (philosophy) , mathematics , measure (data warehouse) , nonlinear system , mathematical analysis , conservation law , calculus (dental) , physics , quantum mechanics , computer science , medicine , philosophy , dentistry , epistemology , database
General one‐parameter families of matrices avoid eigenvalue crossings. It is shown that the matrices associated with the simple waves of nonlinear systems of conservation laws do not obey this rule: a subset of simple waves with nonzero measure has crossing eigenvalues. © 2009 Wiley Periodicals, Inc.