Characteristic matrix values (singular values, eigenvalues, and pivots arising from Gaussian elimination) for the Jacobian matrix and its inverse are considered for maps of real n-space to itself with a nowhere vanishing Jacobian determinant. Bounds on these are related to global invertibility of the map. Polynomial maps with a constant nonzero Jacobian determinant are a special case that allows for sharper characterizations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-2,
author = {L. Andrew Campbell},
title = {Characteristic values of the Jacobian matrix and global invertibility},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {11-20},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-2}
}
L. Andrew Campbell. Characteristic values of the Jacobian matrix and global invertibility. Annales Polonici Mathematici, Tome 77 (2001) pp. 11-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-1-2/