[WIP] HermitianPositiveDefinite

[kellertuer]

I started the HPDs as proposed in #811, but here at home I noticed that programming on a German layout is not something I am used to.

The idea is to

📋

• [ ] introduce as many functions as possible by generalising them from the SPD case.
• [ ] if reasonable maybe even make the SPD case a const of the HPD-HermitianPositiveDefinite{ℝ} case

Check a bit for literature and document carefully. Feel free to check functions as well otherwise I will slowly work through the affine invariant metric.

[mateuszbaran]

Yes, I think the SPD should just be an alias for real-coefficient HPD.

[kellertuer]

Well, if we manage to finish that, for now I struggle a bit to find time to continue, but I will try to continue this step by step though maybe I am a bit slow since for anything beyond checks of points/vectors I first have to read up on the formulae as well.

[codecov[bot]]

Codecov Report

Attention: Patch coverage is 24.56140% with 43 lines in your changes missing coverage. Please review.

Project coverage is 96.24%. Comparing base (453e636) to head (a48e9d9).

Files with missing lines	Patch %	Lines
src/manifolds/HermitianPositiveDefinite.jl	20.37%	43 Missing :warning:

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #813      +/-   ##
==========================================
- Coverage   96.58%   96.24%   -0.34%     
==========================================
  Files         128      129       +1     
  Lines       12178    12231      +53     
==========================================
+ Hits        11762    11772      +10     
- Misses        416      459      +43     

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[mateuszbaran]

No problem, this change is largely independent of the core work of implementing complex HPD.