Principal Components $\mathbf{v}_1$ (Red) and $\mathbf{v}_2$ (Blue) overlayed on centered data.
Eigenvalue Spectrum:
For centered data $\mathbf{X}$, we decompose the covariance matrix $\mathbf{\Sigma}$:
$$ \mathbf{\Sigma} \mathbf{v}_i = \lambda_i \mathbf{v}_i $$
$\lambda_i$ represents the variance explained by the $i$-th component.