[線代] 2x2 complex idempotent matrices
*如果矩陣A滿足 A^2 =A,
則稱矩陣A為idempotent matrix.
又如果矩陣A中的元素屬於複數(Complex)體系,
則稱矩陣A為 complex idempotent matrix.
*題目要我找出所有2x2的complex idempotent matrices,
*我嘗試假定矩陣
A= [a+bi c+di]
[e+fi g+hi] ...(1)
然後想利用A^2=[a+bi c+di] * [a+bi c+di]
[e+fi g+hi] [e+fi g+hi] ...(2)
(1)=(2)的這個條件,搭配複數相等的條件
將a,b,c,d, e,f,g,h的關係式找出來
*但(2)展開之後 整個變得很複雜
a,b,c,d, e,f,g,h的關係式也因此不知道該怎麼找
不知道有沒有板友可以提供一些hint 讓我能想出該怎麼解決這個問題呢
感謝orz
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