Removal of infinite eigenvalues in the generalized matrix eigenvalue problem (Q582809)

The generalized matrix eigenvalue problem (1) \([A(p)-\lambda B(p)]x=0\) is considered, where A, B are complex \(n\times n\) matrices depending on a parameter p, and B is singular. Two main approaches to solve this problem are known. Firstly one considers the reciprocal problem \((B-\mu A)x=0\) and secondly an alternative method which consists in a reduction of the order of (1) to the rank of B in such a manner that the finite eigenvalues of the system are preserved. The authors present an alternative to the ``reciprocal'' and ``reduced'' method which avoids the disadvantages of the former and requires fewer operations than the latter.