Dimensions --- counter-intuitive?

Question

Perhaps I'm misunderstanding the meaning of Dimensions in Mathematica, but the following two examples seem very counter-intuitive to me.

If we define

a = {1,2,3} 
b = {4,5,6} 

then we compute the dimension of its dot product Dimension[ a . b ], I get the "empty" result

{} 

But if I consider instead,

aa = {a1, a2, a3}
bb = {b1, b2, b3} 

and compute the same thing Dimension[ aa . bb ], I get the result

{3} 

Is this behavior to be expected? I understand that the first case has known constants, and while the second case has unknown constants. But regardless, both are simply scalars, and I would expect Dimensions would return the same answer in both cases.

Answer 1

So you would like Dimensions which only respects List head? Good question. -- Kuba

From the documentation:

The "array" is considered full only when it has the same head as at the top:

Dimensions[f[g[x, y], g[a, b], g[s, t]]]
{3}

So I believe, this could be achieved like so:

listDimensions[arg_] := Rest@Dimensions[{arg}]
listDimensions[a.b]
listDimensions[aa.bb]

{}
{}