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2016-01-20 16:36:22 +0200 | asked a question | Dimension of a 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). Please help me.
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, $n\geq 2$. |

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