  The present manuscript aims to derive an expression for the lower bound of
the modulus of the Dirichlet eta function on vertical lines $\Re(s)=\alpha$.
The approach employs concepts of two-dimensional principal component analysis
built on a parametric ellipse, to match the dimensionality of the complex
plane. The one-sided lower bound $\forall s \in \mathbb{C}$ s.t. $\Re(s) \in
\mathcal{P}$, $| \eta(s) | \geq \left| 1 - \frac{\sqrt{2}}{2^\alpha} \right|$,
where $\eta$ is the Dirichlet eta function, is related with the Riemann
hypothesis as $|\eta(s)| > 0$ for any $s \in \mathbb{C}$ s.t. $\Re(s) \in
\mathcal{P}$, where $\mathcal{P}$ is a partition spanning one half of the
critical strip depending upon a variable. We propose the composite lower bound
$\forall s \in \, \mathbb{C}$ s.t. $\Re(s) \in \,]1/2,1[$, $|\eta(s)| \geq
\text{Min}\left(1-
\frac{\sqrt{2}}{2^{\alpha}},\frac{\sqrt{2}}{2^\alpha}-\frac{\sqrt{2}}{2}\right)$,
resulting from transitive composition in $\eta(s) = \left(1-\frac{2}{2^s}
\right) \zeta(s)$. As a founding principle, the solution space of the set of
solutions referring to such $\mathcal{L}^2$-problem is a representation of the
space spanned by explanatory variables satisfying its algebraic form.
