Eigenvalues and Eigenvectors: Generalized and Determinant Free
Jeff Suzuki · Mathematics Magazine · 2020
SummaryThe standard approach to finding eigenvalues relies on solving the characteristic polynomial. But the characteristic polynomial for an n × n matrix will require computing a determinant with n! terms and solving an nth degree polynomial equation, both of which are daunting tasks if n≥3. We present a determinant-free approach which often leads to lower-degree polynomial equations, and which provides a natural introduction to the concept of a generalized eigenvector.