We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in both directions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-8, author = {Hans Havlicek and Peter \v Semrl}, title = {From geometry to invertibility preservers}, journal = {Studia Mathematica}, volume = {173}, year = {2006}, pages = {99-109}, zbl = {1107.47023}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-8} }
Hans Havlicek; Peter Šemrl. From geometry to invertibility preservers. Studia Mathematica, Tome 173 (2006) pp. 99-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm174-1-8/