(1) For A in M_{n╳n}(C), let f: M_{n╳n}(C) ---> M_{n╳n}(C)
defined by f(X) = AX-XA for all X in M_{n╳n}(C). Prove
that f is a linear transformation satisfying
f(XY) = f(X)Y + Xf(Y), for all X, Y in M_{n╳n}(C).
(2) Let f be a linear transformation of the vector space M_{n╳n}(C)
which satisfies
f(XY) = f(X)Y + Xf(Y), for all X, Y in M_{n╳n}(C).
Prove that there is an A in M_{n╳n}(C) such that f(X) = AX-XA.
Note: M_{n╳n}(C) = n 階複係數方陣.
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※ 編輯: PttFund 來自: 219.68.227.219 (09/13 14:03)