van den Essen, Arno ; Parthasarathy, T. (1992) Polynomial maps and a conjecture of Samuelson Linear Algebra and its Applications, 177 . pp. 191-195. ISSN 0024-3795
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Official URL: http://www.sciencedirect.com/science/article/pii/0...
Related URL: http://dx.doi.org/10.1016/0024-3795(92)90327-7
Abstract
Let F:Rn→Rn be a C1-mapping. It was conjectured by Samuelson that if the upper left-hand principal minors of the Jacobian of F do not vanish on Rn, then F is injective. However, in 1965 Gale and Nikaido gave a simple counterexample to the case n = 2. In this paper we show that the Samuelson conjecture is true for polynomial mappings from Cn to Cn. Furthermore, we give a precise description of such maps.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| ID Code: | 90938 |
| Deposited On: | 15 May 2012 09:56 |
| Last Modified: | 15 May 2012 09:56 |
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