[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]

Codecov Report

❌ Patch coverage is 24.56140% with 43 lines in your changes missing coverage. Please review.
✅ Project coverage is 99.56%. Comparing base (0dd163c) to head (7b7f847).

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

Additional details and impacted files

@@             Coverage Diff             @@
##            master     #813      +/-   ##
===========================================
- Coverage   100.00%   99.56%   -0.44%     
===========================================
  Files           98       99       +1     
  Lines         9745     9797      +52     
===========================================
+ Hits          9745     9754       +9     
- Misses           0       43      +43     

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[mateuszbaran]

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