数学，线性代数，转置矩阵问题如图所示，转置不是行列互换吗？请把解题过程写一下，谢谢！ 大一线性代数数学题 矩阵 转置
\u6c42\u6559\u7ebf\u6027\u4ee3\u6570\uff0c\u77e9\u9635\u8f6c\u7f6e\u95ee\u9898\u505a\u6cd5\u662f\u5bf9\u7684\uff0c\u77e9\u9635\u8f6c\u7f6e\u5373\u5c06\u77e9\u9635\u7684\u5bf9\u5e94\u884c\u4e0a\u7684\u6570\u5199\u5230\u5bf9\u5e94\u5217\u4e0a\uff0c\u5373\u7b2c\u4e00\u884c\u4e0a\u6240\u6709\u7684\u6570\u5199\u5230\u7b2c\u4e00\u5217\u4e0a\uff0c\u7b2c\u4e8c\u884c\u4e0a\u6240\u6709\u7684\u6570\u5199\u5230\u7b2c\u4e8c\u5217\u4e0a\uff0c\u4ee5\u6b64\u904d\u5386\u6240\u6709\u77e9\u9635\u4e2d\u7684\u6570\u636e\uff0c\u4e0d\u8fc7\u4f60\u8fd9\u4e2a\u8868\u8ff0\u7b26\u53f7\u662f\u4e0d\u5bf9\u7684\u77e9\u9635\u662f\u786c\u62ec\u53f7\u4e0d\u662f\u4e24\u6761\u7ad6\u7ebf\uff0c\u4e24\u6761\u7ad6\u7ebf\u7684\u662f\u884c\u5217\u5f0f\uff0c\u884c\u5217\u5f0f\u662f\u6ca1\u6709\u8f6c\u7f6e\u7684\uff0c\u53ea\u6709\u77e9\u9635\u624d\u6709\u8f6c\u7f6e\uff0c\u77e9\u9635\u7684\u8f6c\u7f6e\u662f\u77e9\u9635\u7684\u57fa\u672c\u8fd0\u7b97
\u6211\u7528'\u4ee3\u8868\u8f6c\u7f6e\uff0c\u6ce8\u610f\u5230\u03b1\u03b1'\u662f\u4e00\u4e2a\u6570\uff0c\u6240\u4ee5A^2=(E\u2013(2/\u03b1\u03b1')\u03b1'\u03b1)^2
=E^2\u2013(4/\u03b1\u03b1')\u03b1'\u03b1+(4/(\u03b1\u03b1')^2)\u03b1'\u03b1\u03b1'\u03b1
\u5176\u4e2d\u7b2c\u4e09\u9879\u4e2d\u03b1'\u03b1\u03b1'\u03b1\u7528\u7ed3\u5408\u5f8b\u5f97
\u03b1'\u03b1\u03b1'\u03b1=\u03b1'(\u03b1\u03b1')\u03b1=(\u03b1\u03b1')\u03b1'\u03b1
\u56e0\u4e3a\u03b1\u03b1'\u662f\u4e2a\u6570\u53ef\u4ee5\u63d0\u5230\u524d\u9762\uff0c\u4e8e\u662f
A^2=E\u2013(4/\u03b1\u03b1')\u03b1'\u03b1+(4/(\u03b1\u03b1')^2)(\u03b1\u03b1')\u03b1'\u03b1
=E\u2013(4/\u03b1\u03b1')\u03b1'\u03b1+(4/\u03b1\u03b1')\u03b1'\u03b1=E
\u5982\u679c\u89c9\u5f97\u6709\u5e2e\u52a9\u8bf7\u91c7\u7eb3
如图
绛旓細杞疆鍚庣殑鐭╅樀涓庡師鐭╅樀鐨勫叧绯伙細1銆佸鏋淎AT=E锛圗涓哄崟浣嶇煩闃碉紝AT琛ㄧず鈥滅煩闃礎鐨杞疆鐭╅樀鈥濓級鎴朅TA=E锛屽垯n闃跺疄鐭╅樀A绉颁负姝ｄ氦鐭╅樀銆2銆佷竴闃剁煩闃电殑杞疆涓嶅彉銆傛浜ょ煩闃典笉涓瀹氭槸瀹炵煩闃点傚疄姝ｄ氦鐭╅樀锛堝嵆璇ユ浜ょ煩闃典腑鎵鏈夊厓閮芥槸瀹炴暟锛夊彲浠ョ湅鍋氭槸涓绉嶇壒娈婄殑閰夌煩闃碉紝浣嗘槸瀛樺湪涓绉嶅姝ｄ氦鐭╅樀锛屽姝ｄ氦鐭╅樀涓嶆槸閰...
绛旓細鐭╅樀閫嗙殑杞疆锛鏄浆缃悗鐨勯嗙煩闃点傚洜姝ゆ槸(x'x)'鐨勯鐭╅樀锛涔熷嵆x'x锛坸'x鏄绉扮煩闃碉級鐨勯嗙煩闃
绛旓細鐭╅樀杞疆鏄绾挎т唬鏁涓竴涓熀纭涓旈噸瑕佺殑姒傚康锛屽畠鎸囩殑鏄皢鐭╅樀鐨勮鎹㈡垚鍒楋紝鍒楁崲鎴愯銆傚鏋滄湁涓涓 𝑚脳 𝑛m脳n鐨勭煩闃 𝐴A锛屽叾杞疆璁颁綔 𝐴𝑇A T 锛岄偅涔 𝐴𝑇A T 灏嗕細鏄竴涓 𝑛𝑡𝑖𝑚𝑒𝑠&...
绛旓細锛1锛塀^T =(I + 2伪伪^T)^T =I + 2(伪伪^T)^T =I + 2(伪^T)^T伪^T =I + 2伪伪^T =B 鍥犳B鏄绉鐭╅樀 锛2锛塀C=(I + 2伪伪^T)(I-伪伪^T)=I + 2伪伪^T- 伪伪^T - 2伪伪^T伪伪^T =I + 伪伪^T -2伪(伪^T伪)伪^T =I + 伪伪^T -2伪(1/...
绛旓細杩欓噷瑕佺敤鍒颁竴涓畾鐞嗭細鑻ヤ袱涓柟闃礎涓嶣鐨勪箻绉槸鍗曚綅闃碉紝鍒橝涓嶣浜掍负閫鐭╅樀銆傚埄鐢ㄨ繍绠楁ц川鏀瑰啓绛夊紡鍙互寰楀嚭A鐨勭畝鍖栬〃杈惧紡銆備笅鍥剧殑瑙ｇ瓟瑕佺偣璇蜂綘鍙傝冦
绛旓細鍦ㄧ煩闃电殑涓栫晫閲锛岃浆缃鎿嶄綔鎻ず浜嗕竴绯诲垪寮曚汉鍏ヨ儨鐨勬ц川锛屽畠浠鍚鏁板鐨勭懓瀹濓紝涓绾挎т唬鏁鐨勭爺绌舵彁渚涗簡寮哄ぇ鐨勫伐鍏枫傞鍏堬紝鎴戜滑鎺㈣涓涓洿瑙傜殑鐗规р斺杞疆鐭╅樀涔樻硶鐨勫濡欎箣澶勶細 褰撴垜浠皢涓涓煩闃典笌鍏惰浆缃浉涔樻椂锛屽叾缁撴灉骞堕潪鎬绘槸鎴戜滑鎵棰勬兂鐨勯偅鏍凤紝鑰屾槸闅愯棌鐫鏌愮绉╁簭銆傞氳繃褰掔撼璇佹槑锛屾垜浠彲浠ュ彂鐜帮紝瀵逛簬浠绘剰...
绛旓細濡傚浘
绛旓細瀵圭殑锛屽簲鐢ㄤ簡濡備笅鍏紡 (AB)T=(BT)(AT)
绛旓細褰揂涓洪潪濂囧紓鐭╅樀鐨勬椂鍊欙紝杩欎袱鑰呯浉绛夈侫閫嗙殑杞疆涓(A-1)T 锛孉鐨勮浆缃负AT锛屼袱鑰呯浉涔橈細(A-1)T * AT = [A * (A-1)]T = ET = E锛屾晠(A-1)T = (AT)-1 鎴栵細鍦ˋ涓簄闃跺彲閫嗙煩闃电殑鎯呭喌涓嬨傚洜涓哄洜涓鸿浆缃笉鏀瑰彉鐭╅樀鐨勭З锛屾墍浠鍙嗭紝A^T涔熷彲閫嗐傚洜涓(A^-1)^T*A^T=(A*A^-1)^T...
绛旓細鏄殑銆傜敤涓涓洿绠鍗曠殑渚嬪瓙璇存槑锛屽亣濡侫鏄1*2鐭╅樀锛坅,b锛,f瀹氫箟鐩稿悓銆俧鏄1*2鐨勭煩闃电┖闂村埌2*1鐨勭煩闃电┖闂寸殑鏄犲皠銆1*2鐭╅樀绌洪棿鏈変袱涓熀锛(1,0)銆侊紙0,1锛,鍙互楠岃瘉杩欎袱缁勫熀鏄弧瓒绾挎鍙樻崲鐨勫畾涔夌殑銆
