Mathematics Faculty Articles
Document Type
Article
Publication Date
9-10-2020
Publication Title
arXiv
Keywords
Doubly stochastic matrix, Tridiagonal matrix, Pentadiagonal matrix, Completely positive matrix, Positive semidefinite matrix
Abstract
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix A is completely positive and provide examples including how one can change the initial conditions or deal with block matrices, which expands the range of matrices to which our decomposition can be applied. Our decomposition leads us to a number of related results, allowing us to prove that for tridiagonal doubly stochastic matrices, positive semidefiniteness is equivalent to complete positivity (rather than merely being implied by complete positivity). We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete positivity, again illustrated by a number of examples.
NSUWorks Citation
Cao, Lei; McLaren, Darian; and Plosker, Sarah, "Tridiagonal and Pentadiagonal Doubly Stochastic Matrices" (2020). Mathematics Faculty Articles. 300.
https://nsuworks.nova.edu/math_facarticles/300
ORCID ID
0000-0001-7613-7191
ResearcherID
G-7341-2019
Additional Comments
NSERC Discovery rant #: 1174582; Canada Foundation for Innovation grant #: 35711; Canada Research Chairs Program grant #: 231250