We disprove a conjecture made by Rajesh Pereira and Joanna Boneng regarding the upper bound on the number of doubly quasi-stochastic scalings of an n × n positive definite matrix. In doing so, we arrive at the true upper bound for 3 × 3 real matrices, and demonstrate that there is no such bound when n ≥ 4.
@article{bwmeta1.element.doi-10_1515_spma-2016-0014,
author = {George Hutchinson},
title = {On the cardinality of complex matrix scalings},
journal = {Special Matrices},
volume = {4},
year = {2016},
pages = {141-150},
zbl = {1333.15028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0014}
}
George Hutchinson. On the cardinality of complex matrix scalings. Special Matrices, Tome 4 (2016) pp. 141-150. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0014/
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