You're looking for the .*
element-wise, broadcasting multiply operator:
julia> A = [ i + j*im for i=1:3, j=1:4 ]
3x4 Array{Complex{Int64},2}:
1+1im 1+2im 1+3im 1+4im
2+1im 2+2im 2+3im 2+4im
3+1im 3+2im 3+3im 3+4im
julia> v = [1:4]
4-element Array{Int64,1}:
1
2
3
4
julia> w = [1:3]
3-element Array{Int64,1}:
1
2
3
julia> A .* w
3x4 Array{Complex{Int64},2}:
1+1im 1+2im 1+3im 1+4im
4+2im 4+4im 4+6im 4+8im
9+3im 9+6im 9+9im 9+12im
julia> A .* v'
3x4 Array{Complex{Int64},2}:
1+1im 2+4im 3+9im 4+16im
2+1im 4+4im 6+9im 8+16im
3+1im 6+4im 9+9im 12+16im