When minimizing an eigendecomposed quadratic function, slight perturbations to the linear coefficient vector $\mathbf{c}$ can cause disproportionate changes in the true minimizer $\bar{\mathbf{x}}$. The sensitivity of the minimizer to these perturbations depends inversely on the magnitude of the eigenvalues boldsymbol{Lambda}_i of the quadratic matrix. Specifically, if the eigenvalues are large, perturbing $\mathbf{c}$ results in only small changes to the minimizer's coordinates $\bar{x}_i$. Conversely, if the eigenvalues are small, even slight changes to $\mathbf{c}$ can lead to dramatic, sensitive changes in the minimizer. This mathematical insight connects the eigendecomposition of a quadratic function to the definition of the condition number and the fundamental difficulty of ill-conditioned optimization.