Solution branch
= Solution branch
A <solution branch> is a portion of a solution set followed continuously as a <curve>. For $F(u,\lambda)=0$ with $u\in\mathbb R^n$, a full <Jacobian matrix> $[F_u\ F_\lambda]$ of <rank> $n$ makes the nearby solution set a one-dimensional <regular level set>. It need not be a <graph of a function> $u(\lambda)$: a <continuation fold> can obstruct that particular choice of parameter while leaving the <solution branch> regular.