Overview

Every eigenvalue computation in this two-unit sequence, from LA-I's characteristic-polynomial method onward, was carried out by hand for small matrices — solve $\det(A-\lambda I)=0$, a polynomial equation. This topic confronts the practical reality: for any matrix larger than about $4\times4$, the characteristic polynomial has no closed-form root formula (a consequence of Galois theory, beyond this unit's scope), and production software instead uses iterative algorithms that converge to the eigenvalues numerically. This topic builds the standard toolkit — power iteration, inverse iteration, and the QR algorithm — that underlies every eigenvalue and SVD computation performed in practice.