Eigenvector saddlepoints and zero properties of the eigenpolynomial factors

AbstractFor the eigenproblem AP = λBP, in which A and B are of a class of Hermitian matrices which includes correlation matrices, it is shown that the eigenvectors are saddlepoints in a “factored” space. As a result, each eigenvector can be characterized as the solution to a min-max (max-min) optimization problem. For the case when matrices A and B are real, the factored space is shown to be real also. In the process of arriving at these results, some interesting properties of eigenpolynomial zeros are proved