求助
<span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';"><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">不好意思，数学符号在论坛上无法粘贴，所以写的看起来有点罗嗦。小弟我对此题很头疼，恳请高手指点一二。</span><span lang="EN-US"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US"><p><font face="Times New Roman"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span lang="EN-US"><p><font face="Times New Roman"> </font></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">如果下面这个结论成立：对矩阵Ｄ和任意</span><span lang="EN-US"><font face="Times New Roman">e>0</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">，存在可逆</span><span lang="EN-US"><font face="Times New Roman">C</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">（</span><span lang="EN-US"><font face="Times New Roman">C</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">与</span><span lang="EN-US"><font face="Times New Roman">e</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">有关），使</span><font face="Times New Roman"> <span lang="EN-US"><p></p></span></font></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">得</span><span lang="EN-US"><font face="Times New Roman">(CD(C</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的逆</span><span lang="EN-US"><font face="Times New Roman">))</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的２范数＜Ｄ的谱半径＋</span><span lang="EN-US"><font face="Times New Roman">e </font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">．</span><font face="Times New Roman"> <span lang="EN-US"><p></p></span></font></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">能不能证明下面的名题？</span><span lang="EN-US"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">对任意实数</span><span lang="EN-US"><font face="Times New Roman">w </font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">， </span><span lang="EN-US"><font face="Times New Roman">((iwI-A)</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的逆Ｂ</span><span lang="EN-US"><font face="Times New Roman">)</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的谱半径＜１</span><span lang="EN-US"><p></p></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">推出 </span><font face="Times New Roman"> <span lang="EN-US"><p></p></span></font></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">存在矩阵</span><span lang="EN-US"><font face="Times New Roman">C</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">使得：对任意实数</span><span lang="EN-US"><font face="Times New Roman">w </font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">（</span><span lang="EN-US"><font face="Times New Roman">C(iwI-A)</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的逆Ｂ</span><span lang="EN-US"><font face="Times New Roman">(C</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">的逆</span><span lang="EN-US"><font face="Times New Roman">)</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">）的２范数</span><span lang="EN-US"><font face="Times New Roman">?<1<p></p></font></span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">（其中</span><span lang="EN-US"><font face="Times New Roman">I</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">是单位矩阵，</span><span lang="EN-US"><font face="Times New Roman">i</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">是虚数单位</span><span lang="EN-US"><font face="Times New Roman">,A,B</font></span><span style="FONT-FAMILY: 宋体; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman';">是矩阵）．</span></p><p class="MsoNormal" style="MARGIN: 0cm 0cm 0pt;"></p></span>
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