On the Gale-Nikaidô-Inada fundamental theorem on univalence of mappings (Q1920785)
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scientific article; zbMATH DE number 917082
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Gale-Nikaidô-Inada fundamental theorem on univalence of mappings |
scientific article; zbMATH DE number 917082 |
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On the Gale-Nikaidô-Inada fundamental theorem on univalence of mappings (English)
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29 March 1998
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The main result of the paper is the following theorem: For every integer \(n\geq 2\) there are an ellipsoid \(D\subset\mathbb{R}^n\) and a mapping \(F:D\to \mathbb{R}^n\) of class \(C^\infty\) such that each principal minor of the Jacobian matrix \(F'(x)\) is positive but \(F\) is not injective.
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Gale-Nikaidô-Inada fundamental theorem
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univalence
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Jacobian matrix
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