幂等矩阵定义是
C^2=C
设A的标准型为F=
E 0
0 0
即可设A=PFQ,其中P,Q可逆,A=PQQ^{-1}FQ,令B=PQ,B可逆,且令C=Q^{-1}FQ,由于F^2=F,所以C^2=C.
设A为n阶方阵,证明存在一可逆矩阵B及一幂等矩阵C,使A等于BC
设A为n阶方阵,证明存在一可逆矩阵B及一幂等矩阵C,使A等于BC
数学人气:971 ℃时间:2019-10-09 05:44:15
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