Is there is any built-in mechanism in Julia to “view” a scalar quantity, like a number, as an array? I am thinking something like as follows, given that the shape of b and c could be broadcast against A.

A = ones(3, 3)
b = 1
c = ones(3)
A .+ b == A .+ c # works, since b and c can each be broadcast to the shape of A
B = broadcast_to(b, (3,3))
C = broadcast_to(c, (3,3))
A + B == a .+ B # true
A + C == a .+ C # true

I think numpy has a function broadcast_to like I am illustrating here. This could be useful if, e.g., you were solving a matrix equation with a constant vector on the right-hand side.

A = ones(3, 3)
b = broadcast_to(1, (3,))
x = A \ b
x == A .\ ones(3)

Note that, consistent with other broadcast functions, doing A .\ b broadcasts b=1 to a 3x3 matrix of 1s, so A .\ b == A \ ones(3,3).

Yes you are right and thanks for pointing that out – beginner mistake for me thinking about broadcasting backwards.

julia> A = rand(3, 3)
3×3 Matrix{Float64}:
0.96678 0.876051 0.849013
0.966259 0.257086 0.658442
0.818418 0.825752 0.210322
julia> A .\ ones(3,3) == A .\ ones(3) == A .\ 1 # All elementwise inverse of each element of A
true
A \ ones(3,3) == A .\ 1
false