Geodesic
Characteristic values of the Jacobian matrix and global invertibility
L. Andrew Campbell1
1 The 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.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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. 
@article{10_4064_ap76_1_2,
     author = {L. Andrew Campbell},
     title = {Characteristic values of the {Jacobian} matrix
and global invertibility},
     journal = {Annales Polonici Mathematici},
     pages = {11--20},
     publisher = {mathdoc},
     volume = {76},
     number = {1-2},
     year = {2001},
     doi = {10.4064/ap76-1-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap76-1-2/}
}
TY  - JOUR
AU  - L. Andrew Campbell
TI  - Characteristic values of the Jacobian matrix
and global invertibility
JO  - Annales Polonici Mathematici
PY  - 2001
SP  - 11
EP  - 20
VL  - 76
IS  - 1-2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap76-1-2/
DO  - 10.4064/ap76-1-2
LA  - en
ID  - 10_4064_ap76_1_2
ER  - 
%0 Journal Article
%A L. Andrew Campbell
%T Characteristic values of the Jacobian matrix
and global invertibility
%J Annales Polonici Mathematici
%D 2001
%P 11-20
%V 76
%N 1-2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap76-1-2/
%R 10.4064/ap76-1-2
%G en
%F 10_4064_ap76_1_2
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. http://geodesic.mathdoc.fr/articles/10.4064/ap76-1-2/

Cité par Sources :