How To Define An Outer Product (in xAct)?

I am working with xAct / xCoba / xTras and I would like to construct a matrix out of a vector.
So, I have a vector V on a manifold M:

DefManifold[M, 3, IndexRange[a, n]]
DefTensor[V[[Mu]], M]

Now, I would like to take the outer / dyadic product to construct a 4×4 matrix on the manifold M4 by doing something like

{1,B[mu]} * {1,B[nu]}
= 
{{1 , B1    , B2    , B3},
{B1 , B1.B1 , B1.B2 , B1.B3},
{B2 , B2.B1 , B2.B2 , B2.B3},
{B3 , B3.B1 , B3.B2 , B3.B3}}

where * is the outer product and . the scalar (or dot) product between the vector components Bi.

How can this be done? Thank you very much in advance for your reply. 🙂