zeros(Float64, 2) or zeros(2, Float64)

julia> a  = zeros(Float64,  2)
2-element Vector{Float64}:

julia> a  = zeros(2, Float64 )
ERROR: MethodError: no method matching zeros(::Int64, ::Type{Float64})

Closest candidates are:
  zeros(::Union{Integer, AbstractUnitRange}...)
   @ Base array.jl:631

 [1] top-level scope
   @ REPL[15]:1

So the order of the parameters is essential? Is there any rule in construction such typical objects?

Yeah, the type always comes first.

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help?> zeros
search: zeros count_zeros set_zero_subnormals get_zero_subnormals leading_zeros trailing_zeros zero iszero RoundToZero

  zeros([T=Float64,] dims::Tuple)
  zeros([T=Float64,] dims...)

  Create an Array, with element type T, of all zeros with size specified by dims. See also fill, ones, zero.

Yes, zero is a function that constructs an array containing zeros, and the docstring indicates that it takes the element type as an optional first argument.

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zeros([T=Float64,]   dims::Tuple)

means I can invoke the function as

a = zeros(Float64, (2,3))


zeros([T=Float64,]   dims...)

means I can invoke the function as

a = zeros(Float64, 2,3)

Is my understanding right?

That is correct. Inside of a function definition, trailing dots ... indicates a variable number of arguments (docs for Varargs).

In this case zeros(Float64, 2, 3) yields a two-dimensional array of size 2x3, zeros(Float64, 2, 3, 4) yields a three-dimensional array of size 2x3x4, etc.

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Here’s a description of the preferred order of function arguments