Generalize 3-arg dot to HermOrSym

[dkarrasch]

This was unnecessarily restrictive, and didn't handle, e.g., complex symmetric and quaternionic hermitian matrices.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 93.86%. Comparing base (1ffbf9d) to head (16daef9).
⚠️ Report is 15 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1410      +/-   ##
==========================================
- Coverage   93.89%   93.86%   -0.03%     
==========================================
  Files          34       34              
  Lines       15830    15838       +8     
==========================================
+ Hits        14864    14867       +3     
- Misses        966      971       +5     

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[araujoms]

Your PR breaks the 3-argument dot product of Hermitian/Symmetric matrices of matrices, which currently works:

julia> m = Symmetric([randn(ComplexF64, 2, 2) for i in 1:2, j in 1:2]);

julia> x = [randn(ComplexF64, 2) for i in 1:2];

julia> y = [randn(ComplexF64, 2) for i in 1:2];

julia> dot(x,m,y)

[stevengj]

I guess dot is not required to implement an inner product (even in the Hermitian case, we don't require positive-definiteness), so broadening it to complex-symmetric etcetera seems okay.

[stevengj]

That being said, $x^* A y$ is a pretty unnatural operation to perform if $A = A^T$ is complex-symmetric. A more natural operation in that case would be $x^T A y$, i.e. the unconjugated dotu operation (julia#8300).

[dkarrasch]

The complex-symmetric case is more like a byproduct. This is mostly about making the Hermitian case available to non-RealOrComplex. What you're saying, would that be a 3-arg dotu method?