Age-Structured Population Model 2D: Eigenvector Convergence

This is the 2D counterpart to the 3D Leslie-matrix population pyramid — it runs the identical age-structured projection but adds a numerical linear-algebra lens the 3D version only alludes to. Alongside the real population, a normalized "shadow" vector performs pure power iteration on the same projection matrix; its Rayleigh quotient converges to the matrix's true dominant eigenvalue, and the shrinking angle between successive iterations shows, in degrees, exactly when the stable age distribution has been reached. Three linked 2D panels — a population pyramid, a log-scale growth trajectory, and a log-scale eigenvector-convergence trace — turn the abstract Perron–Frobenius argument for why age-structured populations settle into a fixed shape and a constant growth rate into something you can watch converge in real time, including the case (population decline) where the naive growth-rate estimator numerically breaks down but this one does not.