The Practical Evaluation of Eigenvalues and Eigenvectors

Abstract

The problem of determining the eigenvalues and eigenvectors of a matrix has engaged the attention of mathematicians since the middle of the nineteenth century, so it is perhaps not surprising that many methods for solving this problem have been proposed, used, and rejected. Therefore we cannot in the space of one chapter hope to do more than give either a brief survey of the field, or a somewhat more detailed discussion of one or two algorithms; in keeping with our policy of presenting the best methods currently available we elect to do the latter.