Tridiagonal Matrices with Dominant Diagonals and Applications
Operations Research Letters 44, 2016., pp. 231-233
7 Pages Posted: 11 Oct 2014 Last revised: 20 Mar 2016
Date Written: January 8, 2016
We show that in an n×n tridiagonal matrix T that has a positive dominant diagonal and negative super- and sub-diagonals, there exists a strictly positive x>0 that satisfies the system Tx=b, b≧0 and b≠0. Furthermore, if T is symmetric, the components of x can be ranked under certain conditions. We apply these results to characterize the comparative-statics properties in an optimization problem.
Keywords: Tridiagonal Matrix, Dominant Diagonal Matrix, Linear System, Comparative-statics Analysis
JEL Classification: C02, C60
Suggested Citation: Suggested Citation