每週問題 June 18, 2012

本週問題是證明若一 n 階方陣有互異的特徵值,則存在一向量 \mathbf{x} 使得 \mathbf{x},A\mathbf{x},A^2\mathbf{x},\ldots,A^{n-1} 為線性獨立集。

Pow-June-18-12

參考解答

PowSol-June-18-12

This entry was posted in pow 特徵分析, 每週問題 and tagged , , . Bookmark the permalink.

2 Responses to 每週問題 June 18, 2012

  1. Meiyue Shao says:

    利用有理标准型可以得到一个快捷的证明:假定 P^{-1}AP=F 是有理标准型,由条件得 F 只含有一个 Frobenius 块,于是可以取 xP 的第一列(column)。

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