Please, would you give me a hand with this program?
Si scriva una procedura in Sage che calcoli al variare dell'intero n>=2 la
dimensione del sottospazio vettoriale W di End(Mn(R)) costituito da tutte
e sole le applicazioni lineari F(A;B) : Mn(R) --> Mn(R) del tipo
F(A;B) : X |----> AX + XB
al variare di A e B in Mn(R).
Please help me.
Edit: tentative translation:translation contributed by @daniele:
Write a procedure function in Sage which computes, according to the integer n >= 2,
that computes the dimension of the vector subspace W subspace
$W \subseteq \mathrm{End}(M_n(\mathbb{R}))$ constructed as following:
$W$ consists of End(Mn(R)) consisting exactly of
the linear applications F(A; B) maps $F(A;B) \colon M_n(\mathbb{R}) \to M_n(\mathbb{R})$
such that $F(A;B) : Mn(R) --> Mn(R) of type
F(A; B) : \colon X |----> \mapsto AX + XB, for all A and B XB$ with $A$, $B$ in Mn(R).$M_n(\mathbb{R})$.
Here, $n\geq 2$.