= Linear relation
{title2=$\sum_i a_iv_i=0$}
A linear relation among <vectors> $v_1,\ldots,v_n$ is a coefficient tuple $(a_1,\ldots,a_n)$ satisfying $\sum_i a_iv_i=0$. It is nontrivial if at least one coefficient is nonzero. For the <matrix> with these vectors as columns, the space of relations is its <kernel>. The vectors are <linearly independent> exactly when this kernel is zero. An invertible change of coordinates preserves every relation, since $S\sum_i a_iv_i=0$ if and only if $\sum_i a_iv_i=0$.
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