  Evolution algebras with one dimensional square are classified using the
theory of inner product spaces. More precisely, for $A$ an evolution algebra
with $\dim(A^2) = 1$ and $a$ a generator of $A^2$, the product of $A$ is given
by $xy = \langle x,y\rangle a$. Three broad classes of algebras are obtained:
  (1) $a\in\hbox{Ann}(A)$;
  (2) $a\notin\text{Ann}(A)$ and $a$ is isotropic relative to $\langle\cdot,
\cdot\rangle$;
  (3) $a\notin\text{Ann}(A)$ and $a$ is anisotropic relative to $\langle\cdot,
\cdot\rangle$.
