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Add properties to Manifold and metrics
This PR collects and adds properties to manifolds and metrics. addressing #1475
Just to list out manifold properties. @ninamiolane @nguigs @ythanwerdas
- Euclidean : Connected : True, Compact : False
- General Linear : Connected : True, Compact: False (general linear as whole is disconnected, but since we are only instantiating with +det or -det it is always connected)
- Grasmannian : Connected : True, Compact : True (ref : https://en.wikipedia.org/wiki/Grassmannian)
- Heisenberg : Connected : True, Compact : True (ref : https://math.stackexchange.com/questions/434384/the-heisenberg-manifold)
- Hermitian : Connected : True, Compact : False
- Hyperbolic : Connected : True, Compact : False
- Full rank matrices : Not sure
- Full rank correlation matrices : Not Sure
- Hypersphere : Connected : True, Compact : True
- Lower triangular matrices : connected : True, compact : False
- Positive Lower triangular matrices : connected : True, compact : False
- Preshape space : Not Sure
- rank k psd matrices : Not Sure
- skew symmetric : Connected : True, Compact : False
@SaitejaUtpala any update on this? 🙌