Angles between flats

The concept of angles between lines (in the plane or in space), between two planes (dihedral angle) or between a line and a plane can be generalized to arbitrary dimensions. This generalization was first discussed by Camille Jordan.^[1] For any pair of flats in a Euclidean space of arbitrary dimension one can define a set of mutual angles which are invariant under isometric transformation of the Euclidean space. If the flats do not intersect, their shortest distance is one more invariant.^[1] These angles are called canonical^[2] or principal.^[3] The concept of angles can be generalized to pairs of flats in a finite-dimensional inner product space over the complex numbers.

^ ^a ^b Cite error: The named reference jordan was invoked but never defined (see the help page).
^ Cite error: The named reference afriat was invoked but never defined (see the help page).
^ Cite error: The named reference bjoerck was invoked but never defined (see the help page).

[jordan-1] Cite error: The named reference jordan was invoked but never defined (see the help page).

[afriat-2] Cite error: The named reference afriat was invoked but never defined (see the help page).

[bjoerck-3] Cite error: The named reference bjoerck was invoked but never defined (see the help page).

[1]

[2]

[3]