Question: Is it possible to handle matrices of vectors with Maple ?

Hello,

I cannot find a solution for multiplying matrices containing vectors. I seems that matrix operations are not overloaded for accepting vectors. Here is a minimum example :

restart;
with(LinearAlgebra);
with(VectorCalculus);
A := Matrix([u, v]);
B := Transpose(A) . A;

# Entries of A are in fact vectors
u := `<,>`(u1, u2);
v := `<,>`(v1, v2);

# Here are the expected entries of matrix B

u . u;
v . v;
u . v;

# but entries cannot be calculated
simplify(B);

B := Transpose(A) . A;

Of course I can obtain the result if I construct the matrix A with the components of u and v but  my goal is to manipulate more concise expressions with vectors rather than components. May I find a solution in some other package ?

Would it be a complicated task to develop the missing operators or tell Maple to use the dot operator (for matrices and vector) when performing matrix multiplication ?

Thanks for your insights.