Further generalization of symmetric multiplicity theory to the geometric case over a field

Abstract

Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.

Keywords

• combinatorially symmetric matrix
• eigenvalue
• generalized star
• geometric multiplicity
• graph of a matrix
• path
• 05c38
• 05c50 (primary)
• 05c05
• 15a18 (secondary)