Sympy - dot product and norm of symbolic vector

Question

Is there a way to express an symbolic expression involving vectors and operations on them without evaluating them?

from sympy import symbols, acos, MatrixSymbol, Matrix

rA = MatrixSymbol("r^A", 2, 1)
rB = MatrixSymbol("r^B", 2, 1)
rA, rB = Matrix(rA), Matrix(rB) # Basically I want to skip this step
acos((rA.dot(rB)) / rA.norm())

This will evaluate the expression to:

    ⎛r_00__A⋅r_00__B + r_10__A⋅r_10__B ⎞ 
acos⎜─────────────────────────────────⎟
    ⎜      _________________________  ⎟
    ⎜     ╱          2            2   ⎟
    ⎝   ╲╱  │r_00__A│  + │r_10__A│    ⎠

But instead I would like it to evaluate to something like this, while still being able to substitute the symbolic Vectors later on.

    ⎛ r_A⋅r_B ⎞
acos⎜─────────⎟
    ⎝ ||r_A|| ⎠

Answer 1

You could replace .dot and .norm by matrix product : acos(A.T*B/sqrt(A.T*A)).
Minimal working example :

In [1]: from sympy import *
In [2]: init_printing(use_unicode=True)
In [3]: init_printing(use_latex=False)
In [4]: A = MatrixSymbol('A', 2, 1)
In [5]: B = MatrixSymbol('B', 2, 1)
In [6]: acos(A.T*B/sqrt(A.T*A))
Out[6]: 
    ⎛           -1/2⎞
    ⎜ T   ⎛ T  ⎞    ⎟
acos⎝A ⋅B⋅⎝A ⋅A⎠    ⎠