Characteristic values of the Jacobian matrix and global invertibility

Volume 76 / 2001

L. Andrew Campbell 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.


  • L. Andrew CampbellThe Aerospace Corp.
    M1-102 P.O. Box 92957
    Los Angeles, CA 90009, U.S.A.

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