Tridiagonal matrices with dominant diagonals and applications. (English) Zbl 1408.15013
Summary: We show that in an \(n \times n\) 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 \(T x = b\), \(b \geqq 0\) and \(b \ne 0\). 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.
MSC:
| 15B05 | Toeplitz, Cauchy, and related matrices |
Software:
NAPACKReferences:
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