Why is it not allowed to calculate the dot product of two row vectors?
Example:
julia> b=ones(3)'
1×3 RowVector{Float64,Array{Float64,1}}:
1.0 1.0 1.0
julia> a=ones(3)'
1×3 RowVector{Float64,Array{Float64,1}}:
1.0 1.0 1.0
julia> dot(a,b)
ERROR: MethodError: no method matching dot(::RowVector{Float64,Array{Float64,1}}, ::RowVector{Float64,Array{Float64,1}})
julia>
In addition to @Mattriks’s solution, a bit more context: think of RowVectors as matrices to a large extent. See ?RowVector.
I think the error message could be improved with a statement like “Did you mean vecdot?”
I think a dot method should be added for two RowVectors. This is pretty unambiguous mathematically: if x is a vector and x' is a “row vector” (an element of the dual space), then the inner product on the former should define an inner product on the latter.
But if we define dot(a,b) = a’*b one would expect to get back a matrix (the outer product) when a and b are row vectors.
I’d say it should only be defined to return a Number if that’s also the case when a and b are matrices.
I’m skeptical that this should be the definition of dot; it seems like it should be defined to be an inner product, consistent with norm(x) = sqrt(dot(x,x)). Note that norm(x') is already defined to be norm(x) where x is a vector.
(I guess your a'b definition would work too if we defined norm(x) consistent with sqrt(norm(dot(x,x))), but this seems unconventional to me.)
What is the point of defining dot(a,b) = a'b since you can just type a'b if that is what you want?
The problem is that the choice of dot product with general matrices is more ambiguous. Worse, we define a default norm(A) for matrices by the induced norm, but that is not consistent with the most obvious matrix inner product (which would give the Frobenius norm).
dot should always, always be an inner product and never ever an outer product.