Fig. 3

Geometrical interpretation of subspace angles between 2D subspaces of a 3D space. The subspaces are defined by the column span of \(\varvec{Y}, \varvec{Z}\in {\mathbb {R}}^{3 \times 2}\) in the current illustration. \(\theta _0\) and \(\theta _1\) are the two subspace angles, \({\varvec{y}}_0, {\varvec{y}}_1 \in \mathrm {span}(\varvec{Y})\) and \({\varvec{z}}_0, {\varvec{z}}_1 \in \mathrm {span}(\varvec{Z})\) are the corresponding principal vectors