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令e1 = (1,0,...,0)^T,e2 = (0,1,...,0)^T,...,en = (0,0,...,1)^T,------------注：^T表示转置
则(e1,e2,...,en) = E,-----------------------------------------------------------------n阶单位矩阵
因为对任意n维列向量x,都有Ax=0,
所以Ae1 = 0,Ae2 = 0,...,Aen = 0.
于是 A = AE = A(e1,e2,...,en) = (Ae1,Ae2,...,Aen) = (0,0,...,0) = 0.
则(e1,e2,...,en) = E,-----------------------------------------------------------------n阶单位矩阵
因为对任意n维列向量x,都有Ax=0,
所以Ae1 = 0,Ae2 = 0,...,Aen = 0.
于是 A = AE = A(e1,e2,...,en) = (Ae1,Ae2,...,Aen) = (0,0,...,0) = 0.
1年前
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