In “Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra” by Denton et al., the eigenvalue-eigenvector identity was (re)discovered. It can be rewritten in the following manner:
This project reimplements the formula in both MATLAB and C++, throwing in some mischievous comparisons to MATLAB’s eig function, which also produces the eigenvectors of a given matrix. This was provoked by commentary from Cornell University’s Professor A. Townsend during a Linear Algebra lecture, which pondered the idea that this formula may indeed be useful in cases where only a few eigenvectors are needed from large matrices. While I cannot think of such a case in practice, it was an interesting idea to play with.