In 1976, Cameron et al. [2] proved that, if a finite generalized hexagon of order s admits a polarity, then either s or 3s is a perfect square. Their proof used standard eigenvalue arguments. Later on, Ott [3] showed that for a self polar finite thick generalized hexagon of order s, 3s always has to be a perfect square. His proof used Hecke algebras. It was surprising that one had to use this m...

In this paper, we consider the localization of generalized eigenvalues, and we discuss ways in which the Gersgorin set for generalized eigenvalues can be approximated. Earlier, Stewart proposed an approximation using a chordal metric. We will obtain here an improved approximation, and using the concept of generalized diagonal dominance, we prove that the new approximation has some of the basic ...

In this paper, we propose a new approach for the detection of OFDMA and other wideband signals in the context of centralized cooperative spectrum sensing for cognitive radio (CR) applications. The approach is based on the eigenvalues of the received signal covariance matrix whose samples are in the frequency domain. Soft combining of the eigenvalues at the fusion center is the main novelty. Thi...

We study multihomogeneous analytic functions and a multihomogeneous Newton’s method for finding their zeros. We give a convergence result for this iteration and we study two examples: the evaluation map and the generalized eigenvalue problem.

In this literature, the symmetric inverse generalized eigenvalue problem with submatrix constraints and its corresponding optimal approximation problem are studied. A necessary and sufficient condition for solvability is derived, and when solvable, the general solutions are presented.