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Conditions for Eigenvalue Configurations of Two Real Symmetric Matrices: a Symmetric Function Approach by Hong, Hoon; Profili, Daniel; Sendra, J. Rafael is a scholarly article available to read on EtoBox.

What is Conditions for Eigenvalue Configurations of Two Real Symmetric Matrices: a Symmetric Function Approach about?

For two real symmetric matrices, their eigenvalue configuration is the arrangement of their eigenvalues on the real line. We study the problem of determining a quantifier-free necessary and sufficient condition for two real symmetric matrices to realize a given eigenvalue configuration as a generalization of Descartes' rule of signs. We exploit the combinatorial properties of our definition for eigenvalue configuration to reduce a two-polynomial root counting problem into several single-polynomial root counting problems of symmetric polynomials. We then leverage the fundamental theorem of symmetric polynomials to derive a final quantifier-free necessary and sufficient condition for two real symmetric matrices to realize a given eigenvalue configuration.

Author

Hong, Hoon; Profili, Daniel; Sendra, J. Rafael

Published

2023

Language

EN