کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6416542 | 1336832 | 2013 | 6 صفحه PDF | دانلود رایگان |

Doubly nonnegative matrices arise naturally in many setting including Markov random fields (positively banded graphical models) and in the convergence analysis of Markov chains. In this short note, we settle a recent conjecture by C.R. Johnson et al. [Charles R. Johnson, Brian Lins, Olivia Walch, The critical exponent for continuous conventional powers of doubly nonnegative matrices, Linear Algebra Appl. 435 (9) (2011) 2175-2182] by proving that the critical exponent beyond which all continuous conventional powers of n-by-n doubly nonnegative matrices are doubly nonnegative is exactly nâ2. We show that the conjecture follows immediately by applying a general characterization from the literature. We prove a stronger form of the conjecture by classifying all powers preserving doubly nonnegative matrices, and proceed to generalize the conjecture for broad classes of functions. We also provide different approaches for settling the original conjecture.
Journal: Linear Algebra and its Applications - Volume 439, Issue 8, 15 October 2013, Pages 2422-2427