An algorithm for the inertia sets of tree sign patterns

• Author(s): Fonseca, C. M. da ; Mamede, Ricardo
• Date: 2007
• Persistent ID: http://hdl.handle.net/10316/11300
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): Inertia; Sign pattern matrix; Tridiagonal pattern; Trees; Stars; Double stars; 2-generalized stars
• Document Type: Preprint
• Language: English

Description

A matrix whose entries are +, ¡ or 0 is said a sign pattern. The inertia set of an n-by-n symmetric sign pattern A is the set of inertias of all real symmetric matrices with the same sign pattern as A. We present an algorithm to compute the inertia set of any symmetric tree (or acyclic) sign pattern. The procedure generalizes some recent results. Some examples are provided. Centro de Matemática da Universidade Coimbra