Open AccessSign patterns associated with some graphs that allow or require diagonalizability
Author(s) -
Shantanu Das
Publication year - 2022
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2022.5557
Subject(s) - sign (mathematics) , mathematics , matrix (chemical analysis) , path (computing) , tree (set theory) , star (game theory) , combinatorics , computer science , mathematical analysis , materials science , composite material , programming language
The problems of characterizing sign pattern matrices that allow or require diagonalizability are mostly open. In this paper, we introduce the concept of essential index for a tree sign pattern matrix and use it to investigate the allow problem on diagonalizability for sign pattern matrices having their graphs as trees. We characterize sign pattern matrices allowing diagonalizability, whose graphs are star or path. We also give a sufficient condition for sign pattern matrices whose graphs are trees to allow diagonalizability. Further, we give a necessary condition for a sign pattern matrix to require diagonalizability and characterize all star sign pattern matrices that require diagonalizability.