for 1
is X restricted to be a 2x2 one?
2010-03-01 18:25:30 補充:
我想到第2點做
第1點都淨係諗到2個soln....
問題在於, PM不需要學cayleyhamilton的
注意,不能用cayleyhamilton去找I和3I的~
2010-03-01 18:59:47 補充:
for question one
i am thinking how to avoid using Cayleyhamilton thm
(anyway this question should not appear in AL or you are guided to do it)
for question two, see:
If A^2=B
AB=A(A^2)=A^3
BA=(A^2)A=A^3
so A,B commute
圖片參考:
http://i256.photobucket.com/albums/hh182/zilu_photo/sshot-2010-03-01-18-56-53.png
2010-03-01 19:00:22 補充:
a,b,h are any numbers in the complex set
2010-03-02 12:09:17 補充:
ha
i missed the key step
squre the A out
you get a^2=1 ab=0.5 b^2=-ha
solve it yourself~
2010-03-02 12:09:37 補充:
see my solution for question 1
the reason why i don't want to tackle it by
"first principle" is that i don't want to solve those eqts....
so I compare the inverse of them!!
http://i256.photobucket.com/albums/hh182/zilu_photo/img035.jpg
2010-03-02 12:09:39 補充:
By the way i really want to know what is your teacher's suggest method!!