YLL討論網

謝謝你...有時很懷疑自己的頭腦在想什麼???哈!

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mso-hansi-font-family: 'Times New Roman'"#ed_cl#所以#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#T: R^n--.>R^n#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#為#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#onto#ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl##ed_op#o:p#ed_cl# #ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#其實可利用#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#sylvester#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#維度定理來說明這題#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl##ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#nullity(T)+rank(T)=n#ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"#ed_cl#因為#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#T is invertible#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#，所以#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#nullity(T)=0#ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#rank(T)=n #ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt"#ed_cl##ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#P class=MsoNormal style="MARGIN: 0cm 0cm 0pt"#ed_cl##ed_op#SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: 'Times New Roman'; mso-hansi-font-family: 'Times New Roman'"#ed_cl#所以#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#T: R^n--.>R^n#ed_op#/SPAN#ed_cl##ed_op#SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: 新細明體; mso-ascii-font-family: Verdana; mso-hansi-font-family: Verdana"#ed_cl#為#ed_op#/SPAN#ed_cl##ed_op#SPAN lang=EN-US style="FONT-SIZE: 10pt; FONT-FAMILY: Verdana"#ed_cl#onto#ed_op#o:p#ed_cl##ed_op#/o:p#ed_cl##ed_op#/SPAN#ed_cl##ed_op#/P#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

#ed_op#DIV#ed_cl##ed_op#FONT size=2#ed_cl#Prove or disprove :#ed_op#BR#ed_cl#T: R--.>R linear operator, T is invertible <=> T is onto#ed_op#BR#ed_cl##ed_op#BR#ed_cl#我記得算子好像可得其1-1且onto...但就止於這邊...且T可逆==.>其座標化得到的A是可逆則其可逆...就只有想到這幾個線索...希望有高手解惑一下謝謝..#ed_op#/FONT#ed_cl# #ed_op#/DIV#ed_cl#