Eigenvector saddlepoints and zero properties of the eigenpolynomial factors
The author establishes a number of properties of the eigenvectors of the eigenvalue problem \(Ax=\lambda Bx\), where \(A\) and \(B\) are Hermitian \((N+1)\times (N+1)\) matrices with \(B\) positive definite and, for all \(\lambda\) in some interval containing all the eigenvalues, the difference between the upper and lower \(N\times N\) principal submatrices of \(A-\lambda B\) is semidefinite. Some of the results involve polynomials whose coefficients are the components of an eigenvector.
scientific article; zbMATH DE number 1044240