# determinant condition for a sequence of vectors

Let $x_{1},x_{2},...$ be a sequence of $d$ dimensional vectors. Assume that there is a function $C\colon{\mathbb{N}}^{d}\to{\mathbb{R}}\smallsetminus\{0\}$ such that

 $\sum_{\begin{subarray}{c}n_{1}+\cdots+n_{d}=n\\ 0

for every $n\in{\mathbb{N}}$. Then the sequence is contained within a proper linear subspace.

Title determinant condition for a sequence of vectors DeterminantConditionForASequenceOfVectors 2013-03-22 14:33:44 2013-03-22 14:33:44 GeraW (6138) GeraW (6138) 10 GeraW (6138) Result msc 15A15