Metric Problems in Projective and Grassmann Spaces

In this chapter, several metric problems in projective and Grassmann spaces are presented, such as the determination of their congruence order and their superposability order. For that aim, among others, we investigate sets of equiangular lines and sets of equi-isoclinic subspaces in \(F^r\) , where \(F=\mathbb {R}\) , \(\mathbb {C}\) or \(\mathbb {H}\) . It turns out that the construction of these sets is obtained from the construction of some classes of real, complex or quaternionic square matrices.