[理工] 線代
k
Lex N be n*n matrix such that N =O for some integer k.
prove that I+N is invertible.
[pf]:
(I+N)x=0
Nx=-x----(@)
(I+N)=x
k-1
=> N (I+N)x=0
k-1 k k
=>(N +N )x=0 ;N =O
k-1
=>N x=0
=>N N ....Nx=0 ; Nx=-x
=>Nx=0
=>x=0
x is the only solution for I+N,so it is invertible.
這題可以這樣證明嗎??
感謝
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