每週問題 January 17, 2011

Posted on 01/17/2011 by ccjou

本週問題是證明對於任意方陣 A，必存在一可逆矩陣 B 使得 BA 為投影矩陣。

Pow-Jan-17-11

參考解答

PowSol-Jan-17-11

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2 Responses to 每週問題 January 17, 2011

  1. levinc says:
    01/18/2011 at 11:20 am

    請問 A需要對稱嗎？

    Reply
  2. ccjou says:
    01/18/2011 at 12:30 pm

    A 不必是對稱矩陣，問題只要求 BA 是投影矩陣，但未必是正交投影。設 \{v_1,v_2,\ldots,v_n\} 為 \mathbb{R}^n 基底，證明 BAv_i=v_i，i=1,\ldots,k，且 BAv_j=0，j=k+1,k+2,\ldots,n 即等於證出 BA 是投影矩陣。

    Reply

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