Eigengaps for hub-dominant matrices

Abstract

Hub-dominant matrices are natural extensions of hub matrices. In this article we study eigengaps of the Gram matrix associated with a hub-dominant matrix. A class of hub-dominant matrices is then constructed by using equiangular tight frames.

Keywords:

• hub matrices
• eigengaps
• equiangular tight frames
• arrowhead matrices

AMS Subject Classifications::

• 15A42
• 65T60
• 65F15

Acknowledgements

B.W. Suter would like to thank Dr Daubechies for pointing out the relation between the hub-dominant matrices and equiangular tight frames. L. Shen was supported by Air Force Visiting Summer Faculty Program and by the US National Science Foundation under grant DMS-0712827.