det, logdet, logabsdet for Hermitian (Complex) and Symmetric (Real) matrices, maybe also lu?

@andyferris suggested that the above methods should be implemented in the review of #770, I am planning to do this and just wanted to open an issue for discussion.

LinearAlgebra uses Bunch-Kaufman if possible, then falls back to LU. I imagine we would fall back to this above a certain matrix size, to be determined empirically, like everywhere else in the package.

I would appreciate advice on what to do for small matrices. Copying the triangle and then LU may be the simplest solution. Unless there are better suggestions, I would just do this. Incidentally, this would implement LinearAlgebra.lu for Hermitian/Symmetric, which currently errors.

I have never programmer B-K but if it is not too much work and someone has a reference to get me started I would also consider that.

@andreasnoack, I would also appreciate your advice.

Start with the discussion in PR #770 and the referenced LinearAlgebra symmetric.jl implementation. Compare the proposed det, logdet, and logabsdet behavior for Hermitian and Symmetric matrices, including the possible lu fallback, then resolve the small-matrix strategy and size threshold. Done means the intended method set and implementation approach are agreed; the issue does not yet name repository files or tests.