= Minimally dependent vector family
A finite <vector> family is minimally dependent if it is <linearly dependent> and every proper subfamily is <linearly independent>. For $n\geq2$, the family $e_1,\ldots,e_{n-1},\sum_{j=1}^{n-1}e_j$ in $\mathbb R^n$ is an example. The sum supplies a nonzero dependence. If the sum <vector> is omitted, the remaining <vectors> are a coordinate basis; if $e_j$ is omitted, its coordinate in any proposed relation forces the coefficient of the sum <vector> to vanish, then all other coefficients vanish. Every smaller proper subfamily lies in one of these independent $(n-1)$-element subfamilies.
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