row-vector/column-vector products should act like dot products

[stevengj]

If x and y are vectors of the same length, then (x*x')*y works but x*(x'*y) does not (it gives ERROR: no method *(Array{Float64,1},Array{Float64,1})). The latter can only be accomplished with x*dot(x,y).

This is surprising and, I think, undesirable: * should be associative (neglecting floating-point roundoff errors, of course).

Another way of putting it is that x'*y, or any product of a row vector and a column vector, should return a scalar, not a vector of length 1. (And it should probably just call the BLAS dot.)

[andreasnoack]

This has been discussed a few times, I think. At least in #2472. Actually x'*y for vectors x and y already calls dot but wraps it in a vector afterwards.

[stevengj]

At the very least, a column-vector of length 1 should act like a 1×1 matrix for multiplication purposes. e.g. x * [2] should work and be equivalent to 2x.

[toivoh]

I think that it might make sense to demote a length one vector to a scalar
in cases where a vector does not make sense. We know that dimensions can be
added spuriosly (typically by transposition).

[pabloferz]

This works now, right?

[StefanKarpinski]

Yes:

julia> x = rand(3)
3-element Array{Float64,1}:
 0.61878
 0.178213
 0.0933086

julia> y = rand(3)
3-element Array{Float64,1}:
 0.954149
 0.0926293
 0.336523

julia> (x*x')*y
3-element Array{Float64,1}:
 0.394978
 0.113756
 0.0595605

julia> x*(x'*y)
3-element Array{Float64,1}:
 0.394978
 0.113756
 0.0595605