$\bf命题:$设$A \in {M_n}\left( F \right)$,则下列命题等价
$(1)
Fn=N(A)⊕R(A)$ $(2)
N\left( A \right) \cap R\left( A \right) = \left\{ 0 \right\}$
$(3)
N(A2)=N(A)$ $(4)
r\left( {{A^2}} \right) = r\left( A \right)$ $(5)$$R\left( {{A^2}}
\right) = R\left( A \right)$
$\bf命题:$设$A,B,C,D \in L\left( V \right)$且两两可交换,$AC + BD = E$,证明:$KerAB
= KerA \oplus KerB$
时间: 2024-10-25 11:48:32