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The present manuscript aims to derive an expression for the lower bound ofthe modulus of the Dirichlet eta function on vertical lines $\Re(s)=\alpha$.The approach employs concepts of two-dimensional principal component analysisbuilt on a parametric ellipse, to match the dimensionality of the complexplane. 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 Riemannhypothesis 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 thecritical 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 ofsolutions referring to such $\mathcal{L}^2$-problem is a representation of thespace spanned by explanatory variables satisfying its algebraic form.

A lower bound for the modulus of the Dirichlet eta function on a  partition $\mathcal{P}$ from 2-D principal component analysis and transitive  composition