I am looking to gain a deeper understanding of the Grassman, Stiefel, and Flag manifolds but finding good introductory sources so far has eluded me.
I would prefer sources which have:
(1) Concrete examples (2) Exercises to check my understanding (3) Different ways of looking at their topology/manifold structure (as homogeneous spaces and other methods) and how they relate to each other.
I understand that with advanced concepts finding sources which meet the above two criterion can be somewhat difficult, and I don't mind looking through multiple sources at once.
I also understand these are mentioned in "Matrix groups for undergraduates," but not much information is given besides just defining the objects and not very much discussion of how they relate to each other is mentioned.
Any help with sources would be greatly appreciated.