Characteristic values of the Jacobian matrix and global invertibility
Volume 76 / 2001
Annales Polonici Mathematici 76 (2001), 11-20 MSC: Primary 26B10; Secondary 14R15. DOI: 10.4064/ap76-1-2
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.