inconsistent return value of `dot` for empty vectors

[matthias314]

It seems that for non-empty zero vectors, dot consistently returns the zero element of the target type:

julia> x = Complex{Float64}[0]; y = Float64[0];

julia> dot(x, y), dot(-x, y), dot(conj(x), y), dot(x, -y)
(0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im)

For empty vectors, however, this is not always the case:

julia> v = Complex{Float64}[]; w = Float64[];

julia> dot(v, w)
0.0 - 0.0im

The reason are the lines

LinearAlgebra.jl/src/generic.jl

Lines 995 to 997 in b599095

	if lx == 0
	return dot(zero(eltype(x)), zero(eltype(y)))
	end

in dot(x::AbstractArray, y::AbstractArray). Wouldn't it be more consistent to use zero(dot(zero(eltype(x)), zero(eltype(y)))) or maybe just zero(eltype(x))*zero(eltype(y))?

By the way, the above examples also show that the claim

dot is semantically equivalent to sum(dot(vx,vy) for (vx,vy) in zip(x, y))

in the docstring is not correct:

julia> sum(dot(vx,vy) for (vx,vy) in zip(x, y))
0.0 - 0.0im

julia> sum(dot(vx,vy) for (vx,vy) in zip(v, w))
ERROR: ArgumentError: reducing over an empty collection is not allowed; consider supplying `init` to the reducer

[stevengj]

zero(dot(zero(eltype(x)), zero(eltype(y)))) seems fine (with a comment to explain the seemingly redundant zero call).