Abstract
Li et al. [On the period and base of a sign pattern matrix, Linear Algebra Appl. 212/213 (1994) 101–120.] extended the concepts of the base and period from nonnegative matrices to powerful sign pattern matrices. Then, Shao and You [Bound on the basis of irreducible generalized sign pattern matrices, Linear Algebra Appl. 427 (2007) 285–300.] extended the concepts of the base from powerful sign pattern matrices to non-powerful irreducible sign pattern matrices. In this paper we mainly study the kth multi- g base index for non-powerful primitive nearly reducible sign pattern matrices. We obtain sharp upper bounds, together with a complete characterization of the equality cases of the kth multi- g base index for primitive nearly reducible generalized sign pattern matrices. We also show that there exist “gaps” in the kth multi- g base index set of the classes of such matrices.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
