A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1117,
author = {Jo\~ao Lita da Silva and Ant\'onio Manuel Oliveira},
title = {On the matrix form of Kronecker lemma},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {29},
year = {2009},
pages = {233-243},
zbl = {1208.15025},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1117}
}
João Lita da Silva; António Manuel Oliveira. On the matrix form of Kronecker lemma. Discussiones Mathematicae Probability and Statistics, Tome 29 (2009) pp. 233-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1117/
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