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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).

 2 No.2 Revision slelievre 10168 ●8 ●107 ●203 http://carva.org/samue...

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).

Edit: tentative translation:

Write a procedure in Sage which computes, according to the integer n >= 2, the dimension of the vector subspace W of End(Mn(R)) consisting exactly of the linear applications F(A; B) : Mn(R) --> Mn(R) of type F(A; B) : X |----> AX + XB, for all A and B in Mn(R).

 3 No.3 Revision slelievre 10168 ●8 ●107 ●203 http://carva.org/samue...

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).

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, $n\geq 2$.

 4 No.4 Revision slelievre 10168 ●8 ●107 ●203 http://carva.org/samue...

Please, would you give me Dimension of a hand with this program?certain subspace of a matrix space

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).

Write a function in Sage that computes the dimension of the vector subspace $W \subseteq \mathrm{End}(M_n(\mathbb{R}))$ constructed as following: $W$ consists of linear maps $F(A;B) \colon M_n(\mathbb{R}) \to M_n(\mathbb{R})$ such that $F(A;B) : \colon X \mapsto AX + XB$ with $A$, $B$ in $M_n(\mathbb{R})$. Here, $n\geq 2$.