7.5 Computing eigenvalues
In the last chapter, we reached the singular value decomposition, one of the pinnacle results of linear algebra. We laid out the theoretical groundwork to get us to this point.
However, one thing is missing: computing the singular value decomposition in practice. Without this, we can’t reap all the rewards this powerful tool offers. In this section, we’ll develop two methods for this purpose. One offers a deep insight into the behavior of eigenvectors, but it doesn’t work in practice. The other offers excellent performance, but it is hard to understand what is happening behind the formulas. Let’s start with the first one, illuminating how the eigenvectors determine the effects of a linear transformation!
7.5.1 Power iteration for calculating the eigenvectors of real symmetric matrices
If you recall, we discovered the singular value decomposition by tracing the problem back to the spectral decomposition of symmetric matrices. In...
