D. Gale and H. Nikaido, "The Jacobian matrix and global univalence of mappings", Mathematische Annalen159 (1965) 81--93.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....that if OE is a P 0 function, then it is weakly univalent since OE(x) fflx is a P function for each ffl 0, and hence univalent. We mention a famous consequence of Theorem 5 stated for R n (although the result is valid for any open rectangle in R n ) 14] Theorem 6 (Gale Nikaido [7]) Suppose that f is differentiable on R n and the Jacobian matrix f 0 (x) is a nonsingular P 0 matrix for each x. Then f is univalent. We end this section by noting that the Hurwitz theorem of analytic function theory (that if a sequence of univalent analytic functions on an open connected ....

D. Gale and H. Nikaido, "The Jacobian matrix and global univalence of mappings," Mathematische Annalen, 159 (1965) 81-93.

....supported by the DAAD (Deutscher Akademischer Austauschdienst) and partly by SFB 343. 1 Introduction From the point of view of applicability, real P matrices are very interesting. We refer to their role in the linear complementarity problem (see [1] in global invertibility of vector fields [2] and in nonsingularity characterization of interval matrices [6] We recall that a square matrix is called a P matrix if all its principal minors are positive. In [4] Johnson and Tsatsomeros gave a new characterization of this class: an n by n real matrix A is a P matrix if and only if the set ....

D. Gale and H. Nikaido, The Jacobian matrix and global univalence of mappings, Math. Ann. 19:81-93 (1965).

....x T y subject to y = Mx q x; y 0 : The problem of recognizing whether the LCP has a solution is NP complete. 1 We are interested in the problem of finding a solution in special cases where existence is guaranteed. For example, if M has positive principal minors (i.e. M is a P matrix [1]) a unique solution exists for every q. Also, the problem of computing a Nash equilibrium point in a two person game can be reduced to an LCP with q = Gammae = Gamma1; Delta Delta Delta ; Gamma1) T and M = O B T A O # where A and B have positive entries. A solution always exists ....

D. Gale and H. Nikaido, "The Jacobian matrix and global univalence of mappings", Mathematische Annalen 159 (1965) 81--93.

....index i such that i 0 and [M ] i 0, where [M ] i denotes the ith component of the vector M . The corresponding class L contains the class of P matrices since the latter are characterized by the condition that for every nonzero 2 R n , there is an index i such that i [M ] i 0 (see [9]) If M is an L matrix, LCP[M ; q] always has a solution for any q (see [6] A matrix M 2 R n Thetan is called copositive if x T Mx 0 for every x 0. The matrix M is called copositive plus if it is copositive and x 0 and x T Mx = 0 always imply x T (M M T )x = 0 : The class of ....

D. Gale and H. Nikaido, "The Jacobian matrix and global univalence of mappings," Math. Annalen 159 (1965) 81--93.

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D. Gale and H. Nikaido, "The Jacobian matrix and global univalence of mappings", Mathematische Annalen159 (1965) 81--93.

No context found.

D. Gale and H. Nikaido, "The Jacobian matrix and global univalence of mappings," Math. Annalen 159 (1965) 81--93.

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