I En+A I = I En+AT I 吗?为什么? 其中,En为单位矩阵,A为n阶矩阵,AT为A的转置矩阵.如题.谁能帮我证明下.还有,2个矩阵的和的行列式有没有什么拆分公式?

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I En+A I = I En+AT I 吗?为什么? 其中,En为单位矩阵,A为n阶矩阵,AT为A的转置矩阵.如题.谁能帮我证明下.还有,2个矩阵的和的行列式有没有什么拆分公式?

I En+A I = I En+AT I 吗?为什么? 其中,En为单位矩阵,A为n阶矩阵,AT为A的转置矩阵.如题.谁能帮我证明下.还有,2个矩阵的和的行列式有没有什么拆分公式?
I En+A I = I En+AT I 吗?为什么? 其中,En为单位矩阵,A为n阶矩阵,AT为A的转置矩阵.
如题.谁能帮我证明下.还有,2个矩阵的和的行列式有没有什么拆分公式?

I En+A I = I En+AT I 吗?为什么? 其中,En为单位矩阵,A为n阶矩阵,AT为A的转置矩阵.如题.谁能帮我证明下.还有,2个矩阵的和的行列式有没有什么拆分公式?
相等.因为EnT=En;
所以En+AT =EnT+AT =(En+A)T.
因此|En+AT |=|(En+A)T|=|En+A|
一般情况下,矩阵的和的行列式没有特殊的性质,只能先加后求行列式

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