Given a real n×n matrix A, we make some conjectures and prove partial results about the range of the function that maps the n-tuple x into the entrywise kth power of the n-tuple Ax. This is of interest in the study of the Jacobian Conjecture.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-11,
author = {Gianluca Gorni and Halszka Tutaj-Gasi\'nska},
title = {On the span invariant for cubic similarity},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {113-119},
zbl = {1042.15013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-11}
}
Gianluca Gorni; Halszka Tutaj-Gasińska. On the span invariant for cubic similarity. Annales Polonici Mathematici, Tome 77 (2001) pp. 113-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-11/