[理工] [線代] eigenvalue

[compulsory (強迫)]

    1  0  1  2

    8 -1  1  1
A =                          A:4*4 matrix
    0  0  2  1

    0  0  0 -1

求det(A^4- 5A^2 + 2I)

解答 求出eigenvalue為 -1 -1 1 2

-----以下看不懂

並且令f(x)=x^4-5x^2+2

=>A^4-5A^2+2I=f(A)

=>f(A)具eigenvalue f(-1)=-2 f(-1)=-2 f(1)=-2 f(2)=-2

=>det(f(A))=(-2)(-2)(-2)(-2)=16

請問是為什麼呢?

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