Geodesic
Characteristic values of the Jacobian matrix and global invertibility
L. Andrew Campbell1
1The Aerospace Corp. M1-102 P.O. Box 92957 Los Angeles, CA 90009, U.S.A.
Annales Polonici Mathematici, Tome 76 (2001) no. 1-2, pp. 11-20
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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.
DOI : 10.4064/ap76-1-2
Keywords: characteristic matrix values singular values eigenvalues pivots arising gaussian elimination jacobian matrix its inverse considered maps real n space itself nowhere vanishing jacobian determinant bounds these related global invertibility map polynomial maps constant nonzero jacobian determinant special allows sharper characterizations

L. Andrew Campbell  1

1 The Aerospace Corp. M1-102 P.O. Box 92957 Los Angeles, CA 90009, U.S.A. 
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L. Andrew Campbell. Characteristic values of the Jacobian matrix
and global invertibility. Annales Polonici Mathematici, Tome 76 (2001) no. 1-2, pp. 11-20. doi: 10.4064/ap76-1-2

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