Invertible and symmetric or skew-symmetric matrices

[mateuszbaran]

See "ON THE GEOMETRY OF VARIETIES OF INVERTIBLE SYMMETRIC AND SKEW-SYMMETRIC MATRICES". It's a variety instead of a manifold but that just mean we also have to add stratification.

See also JuliaManifolds/Manopt.jl#473 .

[kellertuer]

Would that maybe exceed the main scope of our package? But sure we can start it here and if we notice we want to do more we can move it to its own package that handles more general things than manifolds.

[mateuszbaran]

Depends on the intended functionality IMO. To me handling stratification is within the scope of this package but the algebraic part of varieties should probably be developed separately.

[kellertuer]

Sounds fair. I also have much less clue about the algebraic part, nor whether that was maybe started by someone already.

[mateuszbaran]

The algebraic part is being worked on here for example: https://docs.oscar-system.org/dev/AlgebraicGeometry/intro/ . It's a bit too abstract for me though.