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Zbl 0724.15004
Wolsson, K.
Linear dependence of a function set of m variables with vanishing generalized Wronskians. (English)
[J] Linear Algebra Appl. 117, 73-80 (1989). ISSN 0024-3795

The author considers necessary and sufficient conditions for a set $\phi$ of n functions $\phi\sb i: E\sp m\to E\sp 1$, which together with their partial derivatives of order at least n-1 are continuous, to be linearly dependent. After giving some definitions he shows that the vanishing of all generalized Wronskians of $\phi =(\phi\sb 1(t),...,\phi\sb n(t))$, $(t=(t\sb 1,...,t\sb m))$ in an open set $G\subset E\sp m$ implies that G contains a countable set of disjoint, open, connected components of the interiors of set of constant order such that (1) on each such component $\phi$ is linearly independent, (2) the union of these components is dense in G.
[T.Nôno (Hiroshima)]

MSC 2000:: *15A03 Vector spaces
53A45 Vector and tensor analysis
26B12 Calculus of vector functions

Keywords: linear dependence; functions of several variables; generalized Wronskians

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