推 xx52002 :@@ 為什麼可以直接把x^3-x^2+x-1當作特徵多項式 0.0? 02/28 23:56
→ xx52002 :啊 我知道了 囧 感謝您的回答 02/28 23:57
→ ntust661 :λ 三次方 02/28 23:57
※ 引述《xx52002 (冰清影)》之銘言：
: Suppose A is a 3*3 real matrix such that A^3 = A^2 - A + I
: (a) Find all possible eigenvalues of A.
: (b) Determine the minimal and characteristic polynomial of A.
: (c) Is A diagonalizable? Explain your answer.
: 煩請各位解答 QQ
3 2
λ - λ + λ - 1 = 0 (minimal and characteristic polynomial of A)
λ = 1
λ = i
λ = -i
可以的^^ 因為特徵值對應的特徵向量互相線性獨立
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