How to show that 1 and -1 are the only eigenvalues of T ??
更新1:
個operator係T(A)=A^t
how to find the eigenvalues?
2011-01-24 4:02 am
Let T be the linear operator on Mnxn(R) defined by T(A)=At.
How to show that 1 and -1 are the only eigenvalues of T ??
How to show that 1 and -1 are the only eigenvalues of T ??
回答 (2)
2011-01-24 5:26 am
✔ 最佳答案
By the definition of eigenvalueT(A) = λA
A^T = λA
det (A^T) = det (λA) = (λ^n) det A
Since det (A^T) = det A, this implies that λ^n = 1 => λ = -1 or 1
2011-02-12 9:42 am
你這答案沒考慮到det(A)=0的case呢...
收錄日期: 2021-04-26 14:05:39
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