The critical exponent for continuous conventional powers of doubly nonnegative matrices
Linear Algebra and Its Applications
We prove that there exists an exponent beyond which all continuous conventional powers of n-by-n doubly nonnegative matrices are doubly nonnegative. We show that this critical exponent cannot be less than n - 2 and we conjecture that it is always n - 2 (as it is with Hadamard powering). We prove this conjecture when n < 6 and in certain other special cases. We establish a quadratic bound for the critical exponent in general. (C) 2011 Elsevier Inc. All rights reserved.
Lins, Brian; Johnson, Charles R.; and Walch, Olivia, The critical exponent for continuous conventional powers of doubly nonnegative matrices (2011). Linear Algebra and Its Applications, 435(9), 2175-2182.