Rank-one spectral-factor Gram matrix
= Rank-one spectral-factor Gram matrix
{title2=$M=qq^*$}
For <coefficient> column $q=(q_0,\ldots,q_d)^T$, $M_{ij}=q_i\overline{q_j}$ is a <Hermitian matrix> and a <positive semidefinite matrix> because $x^*Mx=|q^*x|^2$. Expanding $|q(z)|^2$ on the <unit circle> gives <coefficient> $p_k=\sum_{i-j=k}M_{ij}$. Thus $M$ has <matrix rank> one when $q\ne0$ and zero otherwise. General feasible <Gram matrices> need not have <matrix rank> one.