= Linear independence of nonzero orthogonal vectors
{title2=$\langle q_i,q_j\rangle=0\ (i\ne j),\ q_i\ne0$}
A finite collection of nonzero pairwise <orthogonal vectors> is <linearly independent>. Given $\sum_i a_iq_i=0$, take the <inner product> with $q_j$ to obtain $a_j\lVert q_j\rVert^2=0$. Positive definiteness and $q_j\ne0$ force $a_j=0$ for every index. The nonzero condition matters: adjoining a <zero vector> preserves pairwise orthogonality but destroys <linear independence>.
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