Vector{Real} is a type, not an instance of that type. To construct an empty instance, use the zero-argument constructor.
julia> b = Vector{Real}()
Real[]
julia> push!(b, 0.0)
1-element Vector{Real}:
0.0
Unlike in Matlab, a vector is not a matrix: the former has one dimension, the latter has two.
julia> Vector <: AbstractMatrix
false
…and a Vector’s length isn’t encoded in its type signature and is free to vary. StaticArrays.jl provides fixed-length vectors.
julia> dump(ones(3))
Array{Float64}((3,)) [1.0, 1.0, 1.0]
julia> dump(@SVector ones(3))
SVector{3, Float64}
data: Tuple{Float64, Float64, Float64}
1: Float64 1.0
2: Float64 1.0
3: Float64 1.0