作者PttFund (批踢踢基金)
看板Math
标题[线代] 线代(16)
时间Mon Sep 12 08:28:58 2005
(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 阶复系数方阵.
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