A polynomial time spectra decomposition test for certain classes of inverse M-matrices.
Stuart, Jeffrey L. (1998)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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A polynomial time spectra decomposition test for certain classes of inverse M-matrices.
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Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.