[線代] eigenvalue

[mqazz1 (無法顯示)]

Every n*n matrix has n eigenvalues and n eigenvectors
        False

========

(d) Each eigenvector of A is also an eigenvector of A^2
        True

(e) Each eienvector of an invertible matrix A is also an eigenvector of A^(-1)
        True

(f) If v is an eigenvector of an invertible matrix A,

then cv is an eigenvector of A^(-1) for all nonzero scalars c

        True


請問這些是為什麼?

謝謝

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→ a21802      :(d)(A^2)X=A(AX)=A(0)=0