论文标题
四元组和等缘线的紧密框架
Tight frames over the quaternions and equiangular lines
论文作者
论文摘要
我们表明，有限紧密框架的许多理论都可以推广到四局部的矢量空间。这包括变分的特征，群体框架以及投影和统一等效的特征。我们对一组等缘线（Equi-Isoclinic子空间）以及与之相关的组特别感兴趣，以及如何在空间之间移动它们$ \ rd $，$ \ cd $和$ \ hd $。我们讨论了Zauner对equiangular Line的猜想的类似物可能是$ \ hd $的。
We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and the characterisations of projective and unitary equivalence. We are particularly interested in sets of equiangular lines (equi-isoclinic subspaces) and the groups associated with them, and how to move them between the spaces $\Rd$, $\Cd$ and $\Hd$. We discuss what the analogue of Zauner's conjecture for equiangular lines in $\Hd$ might be.
